Finite Group Databasebeta

← Group #13140171

Character table — Group #13140171

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ922222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-100000000-1-1-1-100000000
χ1022222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000111100000000111100000000
χ112222222222222222222222-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000000000000000-1-1-1-1-1-1-1-1
χ122222222222222222222222-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000000000000000000011111111
χ132222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-211111111111122-2-200000000-1-1-1-100000000111100000000
χ142222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-22200000000111100000000-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111000022-2-200000000000000000000-1-1-1-11111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-222000000000000000000001111-1-1-1-1
χ17222-2-2-2-22222-2-2-2-220000002222-2-222-2-2-222-2-2-2222-2-2-2-22000000000000000000002i−2i00000000000000000000002i2i−2i−2i0000
χ18222-2-2-2-22222-2-2-2-220000002222-2-222-2-2-222-2-2-2222-2-2-2-2200000000000000000000−2i2i0000000000000000000000−2i−2i2i2i0000
χ19222-2-2-2-22222-2-2-2-22000000-12-1-11122-2-2-2-1211-2-1-1-11111-1−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i300002i−2i0000000000000000000000−i−iii33−3−3
χ20222-2-2-2-22222-2-2-2-22000000-12-1-11122-2-2-2-1211-2-1-1-11111-1−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i30000−2i2i0000000000000000000000ii−i−i−3−333
χ21222-2-2-2-22222-2-2-2-22000000-12-1-11122-2-2-2-1211-2-1-1-11111-1i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i300002i−2i0000000000000000000000−i−iii−3−333
χ22222-2-2-2-22222-2-2-2-22000000-12-1-11122-2-2-2-1211-2-1-1-11111-1i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i30000−2i2i0000000000000000000000ii−i−i33−3−3
χ2322-222-2-2-222-222-2-2-2000000222-22-22-22-2-2-2-22-2222-222-2-2-200000000000000000000002i−2i0000000000000000000000002i−2i2i−2i
χ2422-222-2-2-222-222-2-2-2000000222-22-22-22-2-2-2-22-2222-222-2-2-20000000000000000000000−2i2i000000000000000000000000−2i2i−2i2i
χ2522-222-2-2-222-222-2-2-2000000-12-11-112-22-2-21-2-112-1-11-1-11113−33−3000033−3−333−3−30000002i−2i00000000000000000000−i3i3−i3i3−ii−ii
χ2622-222-2-2-222-222-2-2-2000000-12-11-112-22-2-21-2-112-1-11-1-11113−33−3000033−3−333−3−3000000−2i2i00000000000000000000i3−i3i3−i3i−ii−i
χ2722-222-2-2-222-222-2-2-2000000-12-11-112-22-2-21-2-112-1-11-1-1111−33−330000−3−333−3−3330000002i−2i00000000000000000000i3−i3i3−i3−ii−ii
χ2822-222-2-2-222-222-2-2-2000000-12-11-112-22-2-21-2-112-1-11-1-1111−33−330000−3−333−3−333000000−2i2i00000000000000000000−i3i3−i3i3i−ii−i
χ2922-2-2-222-222-2-2-222-22i−2i2i2i−2i−2i222-2-222-2-222-2-2-22-222-2-2-222-22i−2i−2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ3022-2-2-222-222-2-2-222-22i−2i2i2i−2i−2i2-12-2-22-111-1-1-21-221-1-1111-1-112i−2i−2i2i−i−iii−i−iiiii−i−i000000000000−i3−i3i3i30000000033−3−300000000
χ3122-2-2-222-222-2-2-222-22i−2i2i2i−2i−2i2-12-2-22-111-1-1-21-221-1-1111-1-112i−2i−2i2i−i−iii−i−iiiii−i−i000000000000i3i3−i3−i300000000−3−33300000000
χ3222-2-2-222-222-2-2-222-22i−2i2i2i−2i−2i-12-111-12-2-2221-21-1-2-1-1111-1-11−iii−i2i2i−2i−2i−i−iiiii−i−i00000000000000000000000000003−3−33i3−i3−i3i3
χ3322-2-2-222-222-2-2-222-22i−2i2i2i−2i−2i-12-111-12-2-2221-21-1-2-1-1111-1-11−iii−i2i2i−2i−2i−i−iiiii−i−i0000000000000000000000000000−333−3−i3i3i3−i3
χ3422-2-2-222-222-2-2-222-2−2i2i−2i−2i2i2i222-2-222-2-222-2-2-22-222-2-2-222-2−2i2i2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ3522-2-2-222-222-2-2-222-2−2i2i−2i−2i2i2i2-12-2-22-111-1-1-21-221-1-1111-1-11−2i2i2i−2iii−i−iii−i−i−i−iii000000000000−i3−i3i3i300000000−3−33300000000
χ3622-2-2-222-222-2-2-222-2−2i2i−2i−2i2i2i2-12-2-22-111-1-1-21-221-1-1111-1-11−2i2i2i−2iii−i−iii−i−i−i−iii000000000000i3i3−i3−i30000000033−3−300000000
χ3722-2-2-222-222-2-2-222-2−2i2i−2i−2i2i2i-12-111-12-2-2221-21-1-2-1-1111-1-11i−i−ii−2i−2i2i2iii−i−i−i−iii00000000000000000000000000003−3−33−i3i3i3−i3
χ3822-2-2-222-222-2-2-222-2−2i2i−2i−2i2i2i-12-111-12-2-2221-21-1-2-1-1111-1-11i−i−ii−2i−2i2i2iii−i−i−i−iii0000000000000000000000000000−333−3i3−i3−i3i3
χ392-222-22-2-22-222-22-2-200000022-22-2-2-2222-2-2-222-22-222-22-2-20000000000000000002i−2i000000000000000000002i−2i2i−2i00000000
χ402-222-22-2-22-222-22-2-200000022-22-2-2-2222-2-2-222-22-222-22-2-2000000000000000000−2i2i00000000000000000000−2i2i−2i2i00000000
χ412-222-22-2-22-222-22-2-20000002-1-22-2-21-1-1-11-21221-11-1-11-11100003−33−33−33−33−33−3002i−2i00000000−i3i3−i3i300000000−ii−ii00000000
χ422-222-22-2-22-222-22-2-20000002-1-22-2-21-1-1-11-21221-11-1-11-11100003−33−33−33−33−33−300−2i2i00000000i3−i3i3−i300000000i−ii−i00000000
χ432-222-22-2-22-222-22-2-20000002-1-22-2-21-1-1-11-21221-11-1-11-1110000−33−33−33−33−33−33002i−2i00000000i3−i3i3−i300000000−ii−ii00000000
χ442-222-22-2-22-222-22-2-20000002-1-22-2-21-1-1-11-21221-11-1-11-1110000−33−33−33−33−33−3300−2i2i00000000−i3i3−i3i300000000i−ii−i00000000
χ452-22-22-22-22-22-22-22-200000022-2222-22-2-22-2-2-2-222-22-22-22-2000000000000000000000000002i−2i000000002i2i−2i−2i000000000000
χ462-22-22-22-22-22-22-22-200000022-2222-22-2-22-2-2-2-222-22-22-22-200000000000000000000000000−2i2i00000000−2i−2i2i2i000000000000
χ472-2-22-2-2222-2-22-2-22200000022-2-2-22-2-22-22222-2-22-2-22-2-2220000000000000000000000002-200000022-2-20000000000000000
χ482-2-22-2-2222-2-22-2-22200000022-2-2-22-2-22-22222-2-22-2-22-2-222000000000000000000000000-22000000-2-2220000000000000000
χ492-2-2-222-222-2-2-222-2200000022-2-22-2-2-2-22-222-2222-2-2-222-2200000000000000002-200000000002-2-2200000000000000000000
χ502-2-2-222-222-2-2-222-2200000022-2-22-2-2-2-22-222-2222-2-2-222-220000000000000000-220000000000-222-200000000000000000000
χ512-2-2-222-222-2-2-222-220000002-1-2-22-2111-112-1-22-1-1111-1-11-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i32-20000000000-111-100000000−i3i3i3−i300000000
χ522-2-2-222-222-2-2-222-220000002-1-2-22-2111-112-1-22-1-1111-1-11-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-2200000000001-1-1100000000i3−i3−i3i300000000
χ532-2-2-222-222-2-2-222-220000002-1-2-22-2111-112-1-22-1-1111-1-11-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i32-20000000000-111-100000000i3−i3−i3i300000000
χ542-2-2-222-222-2-2-222-220000002-1-2-22-2111-112-1-22-1-1111-1-11-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-2200000000001-1-1100000000−i3i3i3−i300000000
χ554444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
χ564444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ57444-4-4-4-44444-4-4-4-440000004-244-4-4-2-22224-2-4-42-2-2-22222-20000000000000000000000000000000000000000000000000000
χ58444-4-4-4-44444-4-4-4-44000000-2-2-2-222-2-2222-2-2222111-1-1-1-11−2i3−2i32i32i30000i3i3i3i3−i3−i3−i3−i3000000000000000000000000000000000000
χ59444-4-4-4-44444-4-4-4-44000000-2-2-2-222-2-2222-2-2222111-1-1-1-112i32i3−2i3−2i30000−i3−i3−i3−i3i3i3i3i3000000000000000000000000000000000000
χ6044-444-4-4-444-444-4-4-40000004-24-44-4-22-222-424-4-2-2-22-2-22220000000000000000000000000000000000000000000000000000
χ6144-444-4-4-444-444-4-4-4000000-2-2-22-22-22-22222-22-211-111-1-1-123−2323−230000−3−333−3−333000000000000000000000000000000000000
χ6244-444-4-4-444-444-4-4-4000000-2-2-22-22-22-22222-22-211-111-1-1-1−2323−2323000033−3−333−3−3000000000000000000000000000000000000
χ6344-4-4-444-444-4-4-444-44i−4i4i4i−4i−4i-2-2-222-2-222-2-2222-2211-1-1-111-1−2i2i2i−2i−2i−2i2i2iii−i−i−i−iii000000000000000000000000000000000000
χ6444-4-4-444-444-4-4-444-4−4i4i−4i−4i4i4i-2-2-222-2-222-2-2222-2211-1-1-111-12i−2i−2i2i2i2i−2i−2i−i−iiiii−i−i000000000000000000000000000000000000
χ654-444-44-4-44-444-44-4-4000000-242-222-4444-42-4-2-2-4-22-2-22-2220000000000000000000000000000000000000000000000000000
χ664-444-44-4-44-444-44-4-4000000-2-22-2222-2-2-2222-2-221-111-11-1-1000023−2323−23−33−33−33−33000000000000000000000000000000000000
χ674-444-44-4-44-444-44-4-4000000-2-22-2222-2-2-2222-2-221-111-11-1-10000−2323−23233−33−33−33−3000000000000000000000000000000000000
χ684-44-44-44-44-44-44-44-40000004-2-44442-222-2-42-4-4-2-22-22-22-220000000000000000000000000000000000000000000000000000
χ694-44-44-44-44-44-44-44-4000000-242-2-2-2-44-4-442-4224-22-22-22-220000000000000000000000000000000000000000000000000000
χ704-44-44-44-44-44-44-44-4000000-2-22-2-2-22-222-22222-21-11-11-11-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ714-44-44-44-44-44-44-44-4000000-2-22-2-2-22-222-22222-21-11-11-11-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ724-4-44-4-4444-4-44-4-4440000004-2-4-4-4422-22-24-24-42-222-222-2-20000000000000000000000000000000000000000000000000000
χ734-4-44-4-4444-4-44-4-444000000-24222-2-4-44-44-24-22-4-222-222-2-20000000000000000000000000000000000000000000000000000
χ744-4-44-4-4444-4-44-4-444000000-2-2222-222-22-2-2-2-2221-1-11-1-111000000003-3-333-3-33000000000000000000000000000000000000
χ754-4-44-4-4444-4-44-4-444000000-2-2222-222-22-2-2-2-2221-1-11-1-11100000000-333-3-333-3000000000000000000000000000000000000
χ764-4-4-444-444-4-4-444-44000000-2422-22-4-4-44-4-242-24-2222-2-22-20000000000000000000000000000000000000000000000000000
χ774-4-4-444-444-4-4-444-44000000-2-222-22222-22-2-22-2-21-1-1-111-110000−2i32i32i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ784-4-4-444-444-4-4-444-44000000-2-222-22222-22-2-22-2-21-1-1-111-1100002i3−2i3−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-1000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000000000-2-2-2-2000011111111000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000000022-2-20000-1-1-1-11111000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000000000-2-22200001111-1-1-1-1000000000000
χ8366-6-6-666-6-3-3333-3-336i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000000−i3i3−i3i33−33−3000000000000
χ8466-6-6-666-6-3-3333-3-336i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000000i3−i3i3−i3−33−33000000000000
χ8566-6-6-666-6-3-3333-3-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000000−i3i3−i3i3−33−33000000000000
χ8666-6-6-666-6-3-3333-3-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000000i3−i3i3−i33−33−3000000000000
χ876-66-66-66-6-33-33-33-330033−3333−33000000000000000000000000000000000000000000000000002i−2i0000−i3i3i3−i3−i−iii000000000000
χ886-66-66-66-6-33-33-33-330033−3333−3300000000000000000000000000000000000000000000000000−2i2i0000i3−i3−i3i3ii−i−i000000000000
χ896-66-66-66-6-33-33-33-3300−3333−3333000000000000000000000000000000000000000000000000002i−2i0000i3−i3−i3i3−i−iii000000000000
χ906-66-66-66-6-33-33-33-3300−3333−333300000000000000000000000000000000000000000000000000−2i2i0000−i3i3i3−i3ii−i−i000000000000
χ916-6-66-6-666-333-333-3-300−3i33i33i3−3i30000000000000000000000000000000000000000000000002-2000000-1-111−i3i3i3−i3000000000000
χ926-6-66-6-666-333-333-3-300−3i33i33i3−3i3000000000000000000000000000000000000000000000000-2200000011-1-1i3−i3−i3i3000000000000
χ936-6-66-6-666-333-333-3-3003i3−3i3−3i33i30000000000000000000000000000000000000000000000002-2000000-1-111i3−i3−i3i3000000000000
χ946-6-66-6-666-333-333-3-3003i3−3i3−3i33i3000000000000000000000000000000000000000000000000-2200000011-1-1−i3i3i3−i3000000000000
χ95121212-12-12-12-1212-6-6-66666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-121212-12-12-12-6-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-121212-1212-12-12-66-6-66-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-12-121212-1212-6666-6-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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