Finite Group Databasebeta

← Group #10591221

Character table — Group #10591221

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222222224444444444444444444444441212121212121212121212121212121212121212121212121818181818181818
order12222222334444666666666666663666666612121212121212121212121212121212444444441212121212121212121212121212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111-1-11-1-11111-1-11111-1-1-1-1-1-1-11-11111-1-1-1-1111-1-111-1-11111-1-1-1-1i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ10111-1-11-1-11111-1-11111-1-1-1-1-1-1-11-11111-1-1-1-1111-1-111-1-11111-1-1-1-1i−ii−i-11-11ii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ11111-1-11-1-11111-1-11111-1-1-1-1-1-1-11-11111-1-1-1-1111-1-111-1-11111-1-1-1-1−ii−ii1-11-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ12111-1-11-1-11111-1-11111-1-1-1-1-1-1-11-11111-1-1-1-1111-1-111-1-11111-1-1-1-1−ii−ii-11-11−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ13111-1-11-1-111-1-1111111-1-1-1-1-1-1-11-11111-1-1-1-11-1-111-1-111-1-1-1-11111i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ14111-1-11-1-111-1-1111111-1-1-1-1-1-1-11-11111-1-1-1-11-1-111-1-111-1-1-1-11111i−i−ii-111-1ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i
χ15111-1-11-1-111-1-1111111-1-1-1-1-1-1-11-11111-1-1-1-11-1-111-1-111-1-1-1-11111−iii−i1-1-11−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ16111-1-11-1-111-1-1111111-1-1-1-1-1-1-11-11111-1-1-1-11-1-111-1-111-1-1-1-11111−iii−i-111-1−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222-1222222-1-12222-1-1-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000000000
χ18222222222-1222222-1-12222-1-1-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000000000
χ19222222222-1-2-2-2-222-1-12222-1-1-1-1-12-1-1-1-1-1-1-1-11111-2-2-2-21111111122-2-20000-1-1-1-111110000000000000000
χ20222222222-1-2-2-2-222-1-12222-1-1-1-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111-2-22200001111-1-1-1-10000000000000000
χ2122222222-122222-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000
χ2222222222-122222-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100000000
χ2322222222-12-2-2-2-2-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000022-2-200000000-1-1-1-1111100000000
χ2422222222-12-2-2-2-2-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-222000000001111-1-1-1-100000000
χ25222-2-22-2-22-122-2-222-1-1-2-2-2-2111-112-1-1-11111-1-1-11122-2-2-1-1-1-111112i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ26222-2-22-2-22-122-2-222-1-1-2-2-2-2111-112-1-1-11111-1-1-11122-2-2-1-1-1-11111−2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ27222-2-22-2-22-1-2-22222-1-1-2-2-2-2111-112-1-1-11111-111-1-1-2-2221111-1-1-1-12i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ28222-2-22-2-22-1-2-22222-1-1-2-2-2-2111-112-1-1-11111-111-1-1-2-2221111-1-1-1-1−2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ29222-2-22-2-2-1222-2-2-1-1221111-2-2-22-2-1-1-1-11111-122-2-2-1-111-1-1-1-1111100002-22-200000000-1-111-1-11100000000
χ30222-2-22-2-2-1222-2-2-1-1221111-2-2-22-2-1-1-1-11111-122-2-2-1-111-1-1-1-111110000-22-220000000011-1-111-1-100000000
χ31222-2-22-2-2-12-2-222-1-1221111-2-2-22-2-1-1-1-11111-1-2-22211-1-11111-1-1-1-100002-2-2200000000-1-11111-1-100000000
χ32222-2-22-2-2-12-2-222-1-1221111-2-2-22-2-1-1-1-11111-1-2-22211-1-11111-1-1-1-10000-222-20000000011-1-1-1-11100000000
χ3322-22-2-22-22200002-22-222-2-222-2-2-2-222-222-2-2-2000000000000000000000000000000000000000000002-22-2
χ3422-22-2-22-22200002-22-222-2-222-2-2-2-222-222-2-2-200000000000000000000000000000000000000000000-22-22
χ3522-2-22-2-222200002-22-2-2-222-2-22-22-222-2-2-222-2000000000000000000000000000000000000000000002i−2i−2i2i
χ3622-2-22-2-222200002-22-2-2-222-2-22-22-222-2-2-222-200000000000000000000000000000000000000000000−2i2i2i−2i
χ372-222-2-2-22220000-22-222-22-22-22-2-2-22-222-22-2-200000000000000000000000000000000000000002-22-20000
χ382-222-2-2-22220000-22-222-22-22-22-2-2-22-222-22-2-20000000000000000000000000000000000000000-22-220000
χ392-22-22-22-2220000-22-22-22-22-22-2-22-22-22-22-22-200000000000000000000000000000000000000002i−2i−2i2i0000
χ402-22-22-22-2220000-22-22-22-22-22-2-22-22-22-22-22-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ412-2-2222-2-2222-22-2-2-2-2-22-2-222-2-22222-2-22-2-2222-22-22-22-222-2-222-2-200000000000000000000000000000000
χ422-2-2222-2-222-22-22-2-2-2-22-2-222-2-22222-2-22-2-222-22-22-22-22-2-222-2-22200000000000000000000000000000000
χ432-2-2222-2-22-12-22-2-2-2112-2-22-111-1-12-111-111-1-1-11-112-22-2-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ442-2-2222-2-22-12-22-2-2-2112-2-22-111-1-12-111-111-1-1-11-112-22-2-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ452-2-2222-2-22-1-22-22-2-2112-2-22-111-1-12-111-111-1-11-11-1-22-2211-1-111-1-100000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ462-2-2222-2-22-1-22-22-2-2112-2-22-111-1-12-111-111-1-11-11-1-22-2211-1-111-1-100000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ472-2-2222-2-2-122-22-211-2-2-111-12-2-222-1-111-111-1-12-22-2-11-11-1-111-1-1110000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ482-2-2222-2-2-122-22-211-2-2-111-12-2-222-1-111-111-1-12-22-2-11-11-1-111-1-1110000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ492-2-2222-2-2-12-22-2211-2-2-111-12-2-222-1-111-111-1-1-22-221-11-111-1-111-1-10000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ502-2-2222-2-2-12-22-2211-2-2-111-12-2-222-1-111-111-1-1-22-221-11-111-1-111-1-10000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ512-2-2-2-2222222-2-22-2-2-2-2-222-2-2222-222-2-2-222-222-2-222-2-2222-2-2-2-22200000000000000000000000000000000
χ522-2-2-2-222222-222-2-2-2-2-2-222-2-2222-222-2-2-222-22-222-2-222-2-2-22222-2-200000000000000000000000000000000
χ532-2-2-2-22222-12-2-22-2-211-222-21-1-1-112-1111-1-11-1-111-12-2-22-1-11111-1-1000000003−3−333−3−330000000000000000
χ542-2-2-2-22222-12-2-22-2-211-222-21-1-1-112-1111-1-11-1-111-12-2-22-1-11111-1-100000000−333−3−333−30000000000000000
χ552-2-2-2-22222-1-222-2-2-211-222-21-1-1-112-1111-1-11-11-1-11-222-211-1-1-1-111000000003−3−33−333−30000000000000000
χ562-2-2-2-22222-1-222-2-2-211-222-21-1-1-112-1111-1-11-11-1-11-222-211-1-1-1-11100000000−333−33−3−330000000000000000
χ572-2-2-2-2222-122-2-2211-2-21-1-11-2222-2-1-1111-1-11-12-2-22-111-1-1-11111-1-10000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ582-2-2-2-2222-122-2-2211-2-21-1-11-2222-2-1-1111-1-11-12-2-22-111-1-1-11111-1-10000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ592-2-2-2-2222-12-222-211-2-21-1-11-2222-2-1-1111-1-11-1-222-21-1-1111-1-1-1-1110000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ602-2-2-2-2222-12-222-211-2-21-1-11-2222-2-1-1111-1-11-1-222-21-1-1111-1-1-1-1110000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ6144444444-2-24444-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-21111111100000000000000000000000000000000
χ6244444444-2-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ63444-4-44-4-4-2-244-4-4-2-2-2-22222222-22-2111-1-1-1-11-2-222-2-2221111-1-1-1-100000000000000000000000000000000
χ64444-4-44-4-4-2-2-4-444-2-2-2-22222222-22-2111-1-1-1-1122-2-222-2-2-1-1-1-1111100000000000000000000000000000000
χ6544-44-4-44-44-200004-4-2244-4-4-2-2222-4-2-22-2-2222000000000000000000000000000000000000000000000000
χ6644-44-4-44-4-240000-224-4-2-22244-4-4-42-2-22-2-2222000000000000000000000000000000000000000000000000
χ6744-44-4-44-4-2-20000-22-22-2-222-2-2222211-111-1-1-1000000003i−3i3i−3i3i−3i3i−3i00000000000000000000000000000000
χ6844-44-4-44-4-2-20000-22-22-2-222-2-2222211-111-1-1-100000000−3i3i−3i3i−3i3i−3i3i00000000000000000000000000000000
χ6944-4-44-4-444-200004-4-22-4-44422-22-2-4-2-2222-2-22000000000000000000000000000000000000000000000000
χ7044-4-44-4-44-240000-224-422-2-2-4-44-442-2-2222-2-22000000000000000000000000000000000000000000000000
χ7144-4-44-4-44-2-20000-22-2222-2-222-22-2211-1-1-111-1000000003i−3i3i−3i−3i3i−3i3i00000000000000000000000000000000
χ7244-4-44-4-44-2-20000-22-2222-2-222-22-2211-1-1-111-100000000−3i3i−3i3i3i−3i3i−3i00000000000000000000000000000000
χ734-444-4-4-444-20000-442-24-44-4-22-222-4-22-2-22-222000000000000000000000000000000000000000000000000
χ744-444-4-4-44-2400002-2-44-22-224-44-4-42-22-2-22-222000000000000000000000000000000000000000000000000
χ754-444-4-4-44-2-200002-22-2-22-22-22-22221-111-11-1-1000000003i−3i−3i3i3i−3i−3i3i00000000000000000000000000000000
χ764-444-4-4-44-2-200002-22-2-22-22-22-22221-111-11-1-100000000−3i3i3i−3i−3i3i3i−3i00000000000000000000000000000000
χ774-44-44-44-44-20000-442-2-44-442-222-2-4-22-22-22-22000000000000000000000000000000000000000000000000
χ784-44-44-44-4-2400002-2-442-22-2-44-4-442-22-22-22-22000000000000000000000000000000000000000000000000
χ794-44-44-44-4-2-200002-22-22-22-22-222-221-11-11-11-1000000003i−3i−3i3i−3i3i3i−3i00000000000000000000000000000000
χ804-44-44-44-4-2-200002-22-22-22-22-222-221-11-11-11-100000000−3i3i3i−3i3i−3i−3i3i00000000000000000000000000000000
χ814-4-4444-4-4-2-24-44-42222-222-2-222-2-2-21-1-11-1-111-22-22-22-2211-1-111-1-100000000000000000000000000000000
χ824-4-4444-4-4-2-2-44-442222-222-2-222-2-2-21-1-11-1-1112-22-22-22-2-1-111-1-11100000000000000000000000000000000
χ834-4-4-4-4444-2-24-4-4422222-2-222-2-2-22-21-1-1-111-11-222-2-222-211-1-1-1-11100000000000000000000000000000000
χ844-4-4-4-4444-2-2-444-422222-2-222-2-2-22-21-1-1-111-112-2-222-2-22-1-11111-1-100000000000000000000000000000000

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