Finite Group Databasebeta

← Group #13140234

Character table — Group #13140234

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order12222222366666664412121212336666666666666636666666121212121212121212121212121212122222444444442244446666666612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111-11-1-1-1111-1-11-1-11-111-1-11111-1-111-1-1-1-111-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-1i−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111-11-1-1-1111-1-11-1-11-111-1-11111-1-111-1-1-1-111-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1-1−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111-11-1-1-1111-1-11-1-11-111-1-11111-1-111-1-1-1-111-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111-11-1-1-1111-1-11-1-11-111-1-11111-1-111-1-1-1-111-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111-11-1-1-1111-1-11-1-1-11-1-1111111-1-111-1-1-1-111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1ii−i−iii−i−i-11−ii−ii11-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111-11-1-1-1111-1-11-1-1-11-1-1111111-1-111-1-1-1-111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1−i−iii−i−iii-11i−ii−i11-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111-11-1-1-1111-1-11-1-1-11-1-1111111-1-111-1-1-1-111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111ii−i−i−i−iii1-1−iii−i-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111-11-1-1-1111-1-11-1-1-11-1-1111111-1-111-1-1-1-111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111−i−iiiii−i−i1-1i−i−ii-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222222-12222-1-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1222200000000220000-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222222222-12222-1-1-1-1-1-12-122-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000111111110000000000000000
χ192222222222222222222222-12-1-1-1-1222222-12-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-1-1222222-12-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-12222-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-2-211-2-21111111111222200000000-2-20000-1-1-1-111110000000000000000
χ222222222222222222-2-2-2-2-2-22-12222-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-2-211-2-21111111111-2-2-2-2000000002200001111-1-1-1-10000000000000000
χ232222222222222222-2-2-2-2-2-2-12-1-1-1-1222222-12-1-1-1-1-1-1-1-1-1-111-2-211-2-2111111110000000022220000-2-20000000000000000-1-1-1-11111
χ242222222222222222-2-2-2-2-2-2-12-1-1-1-1222222-12-1-1-1-1-1-1-1-1-1-111-2-211-2-21111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ25222-22-2-2-2222-2-22-2-22-222-2-22-122-2-2-1-111112-1-2-2-1-1-11111-122-1-1-2-211-1-1-1-1111122-2-2000000002-20000-1-111-1-1110000000000000000
χ26222-22-2-2-2222-2-22-2-22-222-2-22-122-2-2-1-111112-1-2-2-1-1-11111-122-1-1-2-211-1-1-1-11111-2-22200000000-22000011-1-111-1-10000000000000000
χ27222-22-2-2-2222-2-22-2-22-222-2-2-12-1-11122-2-2-2-2-1211-1-1-11111-1-1-12211-2-2-1-1-1-11111000000002i2i−2i−2i00002i−2i0000000000000000−i−iii−i−iii
χ28222-22-2-2-2222-2-22-2-22-222-2-2-12-1-11122-2-2-2-2-1211-1-1-11111-1-1-12211-2-2-1-1-1-1111100000000−2i−2i2i2i0000−2i2i0000000000000000ii−i−iii−i−i
χ29222-22-2-2-2222-2-22-2-2-22-2-2222-122-2-2-1-111112-1-2-2-1-1-11111-1-2-21122-1-11111-1-1-1-122-2-200000000-220000-1-11111-1-10000000000000000
χ30222-22-2-2-2222-2-22-2-2-22-2-2222-122-2-2-1-111112-1-2-2-1-1-11111-1-2-21122-1-11111-1-1-1-1-2-222000000002-2000011-1-1-1-1110000000000000000
χ31222-22-2-2-2222-2-22-2-2-22-2-222-12-1-11122-2-2-2-2-1211-1-1-11111-111-2-2-1-1221111-1-1-1-1000000002i2i−2i−2i0000−2i2i0000000000000000−i−iiiii−i−i
χ32222-22-2-2-2222-2-22-2-2-22-2-222-12-1-11122-2-2-2-2-1211-1-1-11111-111-2-2-1-1221111-1-1-1-100000000−2i−2i2i2i00002i−2i0000000000000000ii−i−i−i−iii
χ3322-22-22-2-222-222-2-2-2000000222-22-22-222-2-2-2-22-222-222-2-2-20000000000000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i0000
χ3422-22-22-2-222-222-2-2-2000000222-22-22-222-2-2-2-22-222-222-2-2-2000000000000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i0000
χ3522-22-22-2-222-222-2-2-2000000-12-11-112-222-2-21-2-11-1-11-1-11113−3003−30033−3−333−3−3000000002i−2i2i−2i0000000000000000000000−ii−ii−i3i3−i3i3
χ3622-22-22-2-222-222-2-2-2000000-12-11-112-222-2-21-2-11-1-11-1-11113−3003−30033−3−333−3−300000000−2i2i−2i2i0000000000000000000000i−ii−ii3−i3i3−i3
χ3722-22-22-2-222-222-2-2-2000000-12-11-112-222-2-21-2-11-1-11-1-1111−3300−3300−3−333−3−333000000002i−2i2i−2i0000000000000000000000−ii−iii3−i3i3−i3
χ3822-22-22-2-222-222-2-2-2000000-12-11-112-222-2-21-2-11-1-11-1-1111−3300−3300−3−333−3−33300000000−2i2i−2i2i0000000000000000000000i−ii−i−i3i3−i3i3
χ3922-2-2-2-22222-2-2-2-222000000222-2-222-2-2-222-2-2-2222-2-2-222-20000000000000000000000002-2-2200000000000000000000002-2-220000
χ4022-2-2-2-22222-2-2-2-222000000222-2-222-2-2-222-2-2-2222-2-2-222-2000000000000000000000000-222-20000000000000000000000-222-20000
χ4122-2-2-2-22222-2-2-2-222000000-12-111-12-2-2-2221-21-1-1-1111-1-113−300−330033−3−3−3−333000000002-2-220000000000000000000000-111-1−333−3
χ4222-2-2-2-22222-2-2-2-222000000-12-111-12-2-2-2221-21-1-1-1111-1-113−300−330033−3−3−3−33300000000-222-200000000000000000000001-1-113−3−33
χ4322-2-2-2-22222-2-2-2-222000000-12-111-12-2-2-2221-21-1-1-1111-1-11−33003−300−3−33333−3−3000000002-2-220000000000000000000000-111-13−3−33
χ4422-2-2-2-22222-2-2-2-222000000-12-111-12-2-2-2221-21-1-1-1111-1-11−33003−300−3−33333−3−300000000-222-200000000000000000000001-1-11−333−3
χ452-222-2-22-22-222-2-22-200000022-2222-222-22-2-2-2-2-22-222-22-2-2000000000000000000002i−2i2i−2i0000000000000000002i−2i2i−2i000000000000
χ462-222-2-22-22-222-2-22-200000022-2222-222-22-2-2-2-2-22-222-22-2-200000000000000000000−2i2i−2i2i000000000000000000−2i2i−2i2i000000000000
χ472-22-2-22-222-22-22-2-2200000022-22-2-2-22-22-22-2-2222-22-22-22-2000000000000000000002-2-220000000000000000002-2-22000000000000
χ482-22-2-22-222-22-22-2-2200000022-22-2-2-22-22-22-2-2222-22-22-22-200000000000000000000-222-2000000000000000000-222-2000000000000
χ492-2-222-2-222-2-22-22-2200000022-2-22-2-2-22-2-2222-222-2-22-2-22200000000000000002-22-2000000000000002-22-200000000000000000000
χ502-2-222-2-222-2-22-22-2200000022-2-22-2-2-22-2-2222-222-2-22-2-2220000000000000000-22-2200000000000000-22-2200000000000000000000
χ512-2-222-2-222-2-22-22-220000002-1-2-22-211-111-12-1-22-111-111-1-100−i3i300−i3i3−i3i3−i3i3−i3i3−i3i32-22-200000000000000-11-11−i3i3−i3i30000000000000000
χ522-2-222-2-222-2-22-22-220000002-1-2-22-211-111-12-1-22-111-111-1-100−i3i300−i3i3−i3i3−i3i3−i3i3−i3i3-22-22000000000000001-11-1i3−i3i3−i30000000000000000
χ532-2-222-2-222-2-22-22-220000002-1-2-22-211-111-12-1-22-111-111-1-100i3−i300i3−i3i3−i3i3−i3i3−i3i3−i32-22-200000000000000-11-11i3−i3i3−i30000000000000000
χ542-2-222-2-222-2-22-22-220000002-1-2-22-211-111-12-1-22-111-111-1-100i3−i300i3−i3i3−i3i3−i3i3−i3i3−i3-22-22000000000000001-11-1−i3i3−i3i30000000000000000
χ552-2-2-2222-22-2-2-2222-200000022-2-2-22-2-2-222-2222-22-2-2-222-2200000000000000002-2-22000000000000002-2-2200000000000000000000
χ562-2-2-2222-22-2-2-2222-200000022-2-2-22-2-2-222-2222-22-2-2-222-220000000000000000-222-200000000000000-222-200000000000000000000
χ572-2-2-2222-22-2-2-2222-20000002-1-2-2-22111-1-112-12-2-1111-1-11-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i32-2-2200000000000000-111-1−i3i3i3−i30000000000000000
χ582-2-2-2222-22-2-2-2222-20000002-1-2-2-22111-1-112-12-2-1111-1-11-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i3-222-2000000000000001-1-11i3−i3−i3i30000000000000000
χ592-2-2-2222-22-2-2-2222-20000002-1-2-2-22111-1-112-12-2-1111-1-11-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i32-2-2200000000000000-111-1i3−i3−i3i30000000000000000
χ602-2-2-2222-22-2-2-2222-20000002-1-2-2-22111-1-112-12-2-1111-1-11-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i3-222-2000000000000001-1-11−i3i3i3−i30000000000000000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ63444-44-4-4-4444-4-44-4-44-444-4-4-2-2-2-222-2-22222-2-222111-1-1-1-11-2-2-2-222221111-1-1-1-1000000000000000000000000000000000000000000
χ64444-44-4-4-4444-4-44-4-4-44-4-444-2-2-2-222-2-22222-2-222111-1-1-1-112222-2-2-2-2-1-1-1-11111000000000000000000000000000000000000000000
χ6544-44-44-4-444-444-4-4-40000004-24-44-4-22-2-222-424-4-2-22-2-22220000000000000000000000000000000000000000000000000000000000
χ6644-44-44-4-444-444-4-4-4000000-2-2-22-22-22-2-22222-2211-111-1-1-123−230023−2300−3−333−3−333000000000000000000000000000000000000000000
χ6744-44-44-4-444-444-4-4-4000000-2-2-22-22-22-2-22222-2211-111-1-1-1−232300−23230033−3−333−3−3000000000000000000000000000000000000000000
χ6844-4-4-4-44444-4-4-4-4440000004-24-4-44-2222-2-2-42-44-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ6944-4-4-4-44444-4-4-4-444000000-2-2-222-2-2222-2-2222-211-1-1-111-123−2300−232300−3−33333−3−3000000000000000000000000000000000000000000
χ7044-4-4-4-44444-4-4-4-444000000-2-2-222-2-2222-2-2222-211-1-1-111-1−23230023−230033−3−3−3−333000000000000000000000000000000000000000000
χ714-444-4-44-44-444-4-44-40000004-2-44442-2-22-22-42-4-4-22-2-22-2220000000000000000000000000000000000000000000000000000000000
χ724-444-4-44-44-444-4-44-4000000-242-2-2-2-444-44-42-422-22-2-22-2220000000000000000000000000000000000000000000000000000000000
χ734-444-4-44-44-444-4-44-4000000-2-22-2-2-22-2-22-2222221-111-11-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000000000
χ744-444-4-44-44-444-4-44-4000000-2-22-2-2-22-2-22-2222221-111-11-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000000000
χ754-44-4-44-444-44-44-4-440000004-2-44-4-42-22-22-2-4244-22-22-22-220000000000000000000000000000000000000000000000000000000000
χ764-44-4-44-444-44-44-4-44000000-242-222-44-44-442-4-2-2-22-22-22-220000000000000000000000000000000000000000000000000000000000
χ774-44-4-44-444-44-44-4-44000000-2-22-2222-22-22-222-2-21-11-11-11-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000000000
χ784-44-4-44-444-44-44-4-44000000-2-22-2222-22-22-222-2-21-11-11-11-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000000000
χ794-4-444-4-444-4-44-44-44000000-2422-22-4-44-4-44-242-2-222-222-2-20000000000000000000000000000000000000000000000000000000000
χ804-4-444-4-444-4-44-44-44000000-2-222-2222-222-2-2-22-21-1-11-1-11100−2i32i300−2i32i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000000000
χ814-4-444-4-444-4-44-44-44000000-2-222-2222-222-2-2-22-21-1-11-1-111002i3−2i3002i3−2i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000000000
χ824-4-4-4444-44-4-4-4444-4000000-24222-2-4-4-444-4-24-22-2222-2-22-20000000000000000000000000000000000000000000000000000000000
χ834-4-4-4444-44-4-4-4444-4000000-2-2222-2222-2-22-2-2-221-1-1-111-1100−2i32i3002i3−2i3i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000000000
χ844-4-4-4444-44-4-4-4444-4000000-2-2222-2222-2-22-2-2-221-1-1-111-11002i3−2i300−2i32i3−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000002222000000220000000000-1-1-1-1-1-1-1-100000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000-2-2-2-2000000-2-200000000001111111100000000
χ8766666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000002222000000-2-20000000000-1-1-1-1111100000000
χ8866666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000-2-2-2-20000002200000000001111-1-1-1-100000000
χ89666-66-6-6-6-3-3-333-3336-6-3-333000000000000000000000000000000000000000000002i2i−2i−2i0000002i−2i0000000000−i−iii−i−iii00000000
χ90666-66-6-6-6-3-3-333-3336-6-3-33300000000000000000000000000000000000000000000−2i−2i2i2i000000−2i2i0000000000ii−i−iii−i−i00000000
χ91666-66-6-6-6-3-3-333-333-6633-3-3000000000000000000000000000000000000000000002i2i−2i−2i000000−2i2i0000000000−i−iiiii−i−i00000000
χ92666-66-6-6-6-3-3-333-333-6633-3-300000000000000000000000000000000000000000000−2i−2i2i2i0000002i−2i0000000000ii−i−i−i−iii00000000
χ936-666-6-66-6-33-3-333-330033−3333−33000000000000000000000000000000000000000000002i−2i2i−2i000000000000000000−ii−ii−i3i3−i3i300000000
χ946-666-6-66-6-33-3-333-330033−3333−3300000000000000000000000000000000000000000000−2i2i−2i2i000000000000000000i−ii−ii3−i3i3−i300000000
χ956-666-6-66-6-33-3-333-3300−3333−3333000000000000000000000000000000000000000000002i−2i2i−2i000000000000000000−ii−iii3−i3i3−i300000000
χ966-666-6-66-6-33-3-333-3300−3333−333300000000000000000000000000000000000000000000−2i2i−2i2i000000000000000000i−ii−i−i3i3−i3i300000000
χ976-66-6-66-66-33-33-333-30033−33−3333000000000000000000000000000000000000000000002-2-22000000000000000000-111-1−333−300000000
χ986-66-6-66-66-33-33-333-30033−33−333300000000000000000000000000000000000000000000-222-20000000000000000001-1-113−3−3300000000
χ996-66-6-66-66-33-33-333-300−333333−33000000000000000000000000000000000000000000002-2-22000000000000000000-111-13−3−3300000000
χ1006-66-6-66-66-33-33-333-300−333333−3300000000000000000000000000000000000000000000-222-20000000000000000001-1-11−333−300000000
χ1011212-1212-1212-12-12-6-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12-12-121212-6-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-121212-12-1212-666-66-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-12121212-12-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).