Finite Group Databasebeta

← Group #11800021

Character table — Group #11800021

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222222222444444444444444444444444888888888888888888888242424242424242424242424242424242424242424242424144144
order12233446612121212234666666688121212121212121224242424666812121224242424242424242424242424248888161616162424242424242424484848484848484844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111-11-111-1-1111111-1-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1
χ61111111111111-11-111-1-1111111-1-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11
χ71111111111111-11-111-1-1111111-1-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11
χ81111111111111-11-111-1-1111111-1-1111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1
χ922222222222222222222222-2-222222222-2-2-2-2222-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000
χ102222222222222-22-222-2-2222-2-22-2-222222-2-2-2-2-2-2-22-2-2-222-2-2-2-2-2-222222200000000000000000000000000
χ1122222-2-222-2-2-2-222-2222222200-2-2-2-2-2-2-2-200002220-2-2-2000000000000000000−i2i2−i2i200000000−i2−i2i2i2−i2−i2i2i200
χ1222222-2-222-2-2-2-222-2222222200-2-2-2-2-2-2-2-200002220-2-2-2000000000000000000i2−i2i2−i200000000i2i2−i2−i2i2i2−i2−i200
χ1322222-2-222-2-2-2-2-22222-2-222200-222-2-2-2-2-20000-2-2-20222000000000000000000−i2i2i2−i200000000−i2−i2i2i2i2i2−i2−i200
χ1422222-2-222-2-2-2-2-22222-2-222200-222-2-2-2-2-20000-2-2-20222000000000000000000i2−i2−i2i200000000i2i2−i2−i2−i2−i2i2i200
χ152222-1222-122-1-12-122-1-1-1-1-1-1222-1-1-1-1-1-1-122222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000
χ162222-1222-122-1-12-122-1-1-1-1-1-1222-1-1-1-1-1-1-122222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000
χ172222-1222-122-1-12-122-1-1-1-1-1-1-2-22-1-1-1-1-1-1-1-2-2-2-22-1-1-22-1-1-2-211111111111100000000−i3−i3i3i3−i3−i3i3i30000000000
χ182222-1222-122-1-12-122-1-1-1-1-1-1-2-22-1-1-1-1-1-1-1-2-2-2-22-1-1-22-1-1-2-211111111111100000000i3i3−i3−i3i3i3−i3−i30000000000
χ192222-1222-122-1-1-2-1-22-111-1-1-122211-1-1-1-1-12222-211-2-211-2-2-1-1-1-1-1-111111122-2-20000-1-1-1-111110000000000
χ202222-1222-122-1-1-2-1-22-111-1-1-122211-1-1-1-1-12222-211-2-211-2-2-1-1-1-1-1-1111111-2-22200001111-1-1-1-10000000000
χ212222-1222-122-1-1-2-1-22-111-1-1-1-2-2211-1-1-1-1-1-2-2-2-2-2112-21122111111-1-1-1-1-1-100000000−i3−i3i3i3i3i3−i3−i30000000000
χ222222-1222-122-1-1-2-1-22-111-1-1-1-2-2211-1-1-1-1-1-2-2-2-2-2112-21122111111-1-1-1-1-1-100000000i3i3−i3−i3−i3−i3i3i30000000000
χ23222-1222-12-1-1222-12-1222-1-1-122-122-1-12-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-122-1-1-1-10000222200000000-1-1-1-1-1-1-1-100
χ24222-1222-12-1-1222-12-1222-1-1-122-122-1-12-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-2-2-2000000001111111100
χ25222-1222-12-1-1222-12-1222-1-1-1-2-2-122-1-12-1-11111-1-1-1-2-1-1-111-2-21111-2-2111100000000000000003−33−33−33−300
χ26222-1222-12-1-1222-12-1222-1-1-1-2-2-122-1-12-1-11111-1-1-1-2-1-1-111-2-21111-2-211110000000000000000−33−33−33−3300
χ27222-1222-12-1-122-2-1-2-12-2-2-1-1-122-1-2-2-1-12-1-1-1-1-1-1111-21111122-1-1-1-1-2-21111000022-2-200000000-1-1-1-1111100
χ28222-1222-12-1-122-2-1-2-12-2-2-1-1-122-1-2-2-1-12-1-1-1-1-1-1111-21111122-1-1-1-1-2-211110000-2-222000000001111-1-1-1-100
χ29222-1222-12-1-122-2-1-2-12-2-2-1-1-1-2-2-1-2-2-1-12-1-111111112111-1-1-2-2111122-1-1-1-100000000000000003−33−3−33−3300
χ30222-1222-12-1-122-2-1-2-12-2-2-1-1-1-2-2-1-2-2-1-12-1-111111112111-1-1-2-2111122-1-1-1-10000000000000000−33−333−33−300
χ31222-12-2-2-1211-2-22-1-2-1222-1-1-1001-2-211-21133−3−3-1-1-101113−30033−3−30033−3−30000−i2i2−i2i200000000ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300
χ32222-12-2-2-1211-2-22-1-2-1222-1-1-1001-2-211-21133−3−3-1-1-101113−30033−3−30033−3−30000i2−i2i2−i200000000−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300
χ33222-12-2-2-1211-2-22-1-2-1222-1-1-1001-2-211-211−3−333-1-1-10111−3300−3−33300−3−3330000−i2i2−i2i200000000ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700
χ34222-12-2-2-1211-2-22-1-2-1222-1-1-1001-2-211-211−3−333-1-1-10111−3300−3−33300−3−3330000i2−i2i2−i200000000−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700
χ35222-12-2-2-1211-2-2-2-12-12-2-2-1-1-10012211-21133−3−31110-1-1-1−330033−3−300−3−3330000−i2i2i2−i200000000ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300
χ36222-12-2-2-1211-2-2-2-12-12-2-2-1-1-10012211-21133−3−31110-1-1-1−330033−3−300−3−3330000i2−i2−i2i200000000−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300
χ37222-12-2-2-1211-2-2-2-12-12-2-2-1-1-10012211-211−3−3331110-1-1-13−300−3−3330033−3−30000−i2i2i2−i200000000ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700
χ38222-12-2-2-1211-2-2-2-12-12-2-2-1-1-10012211-211−3−3331110-1-1-13−300−3−3330033−3−30000i2−i2−i2i200000000−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700
χ3922-2222-22222-2-2020-2-200-2-222-2-200-2-22222-22-20000000002-22-22-2000000002i−2i000000002i−2i2i−2i0000000000
χ4022-2222-22222-2-2020-2-200-2-222-2-200-2-22222-22-20000000002-22-22-200000000−2i2i00000000−2i2i−2i2i0000000000
χ4122-2222-22222-2-2020-2-200-2-22-22-200-2-2222-22-22000000000-22-22-220000002i−2i0000002i−2i2i−2i00000000000000
χ4222-2222-22222-2-2020-2-200-2-22-22-200-2-2222-22-22000000000-22-22-22000000−2i2i000000−2i2i−2i2i00000000000000
χ4322-22-12-22-122110-10-21−i3i311-12-2-2−i3i311-1-1-12-22-20−i3i300−i3i300-11-11-11−i3i3−i3i3−i3i3002i−2i00003−3−33−ii−ii0000000000
χ4422-22-12-22-122110-10-21−i3i311-12-2-2−i3i311-1-1-12-22-20−i3i300−i3i300-11-11-11−i3i3−i3i3−i3i300−2i2i0000−333−3i−ii−i0000000000
χ4522-22-12-22-122110-10-21−i3i311-1-22-2−i3i311-1-1-1-22-220−i3i300−i3i3001-11-11-1i3−i3i3−i3i3−i32i−2i000000−ii−ii3−3−330000000000
χ4622-22-12-22-122110-10-21−i3i311-1-22-2−i3i311-1-1-1-22-220−i3i300−i3i3001-11-11-1i3−i3i3−i3i3−i3−2i2i000000i−ii−i−333−30000000000
χ4722-22-12-22-122110-10-21i3−i311-12-2-2i3−i311-1-1-12-22-20i3−i300i3−i300-11-11-11i3−i3i3−i3i3−i3002i−2i0000−333−3−ii−ii0000000000
χ4822-22-12-22-122110-10-21i3−i311-12-2-2i3−i311-1-1-12-22-20i3−i300i3−i300-11-11-11i3−i3i3−i3i3−i300−2i2i00003−3−33i−ii−i0000000000
χ4922-22-12-22-122110-10-21i3−i311-1-22-2i3−i311-1-1-1-22-220i3−i300i3−i3001-11-11-1−i3i3−i3i3−i3i32i−2i000000−ii−ii−333−30000000000
χ5022-22-12-22-122110-10-21i3−i311-1-22-2i3−i311-1-1-1-22-220i3−i300i3−i3001-11-11-1−i3i3−i3i3−i3i3−2i2i000000i−ii−i3−3−330000000000
χ514444-2-4-44-2-4-4224-2-44-2-2-2-2-2-200-4222222200004-2-20-4220000000000000000000000000000000000000000
χ524444-2-4-44-2-4-422-4-244-222-2-2-200-4-2-2222220000-42204-2-20000000000000000000000000000000000000000
χ53444-2-244-2-2-2-2-2-2414-2-2-2-211144-2-2-211-211-2-2-2-2-2114-211-2-2-2-21111-2-2111100000000000000000000000000
χ54444-2-244-2-2-2-2-2-2414-2-2-2-2111-4-4-2-2-211-2112222-211-4-2112222-1-1-1-122-1-1-1-100000000000000000000000000
χ55444-2-244-2-2-2-2-2-2-41-4-2-22211144-22211-211-2-2-2-22-1-1-42-1-122-2-2111122-1-1-1-100000000000000000000000000
χ56444-2-244-2-2-2-2-2-2-41-4-2-222111-4-4-22211-21122222-1-142-1-1-2-222-1-1-1-1-2-2111100000000000000000000000000
χ57444-2-2-4-4-2-2222241-4-2-2-2-211100222-1-12-1-12323−23−23-21102-1-123−2300−3−33300−3−33300000000000000000000000000
χ58444-2-2-4-4-2-2222241-4-2-2-2-211100222-1-12-1-1−23−232323-21102-1-1−23230033−3−30033−3−300000000000000000000000000
χ59444-2-2-4-4-2-22222-414-2-222111002-2-2-1-12-1-12323−23−232-1-10-211−232300−3−3330033−3−300000000000000000000000000
χ60444-2-2-4-4-2-22222-414-2-222111002-2-2-1-12-1-1−23−2323232-1-10-21123−230033−3−300−3−33300000000000000000000000000
χ6144-444-4444-4-444040-4-400-4-440040044-4-4-4000000000000000000000000000000000000000000000000000
χ6244-44-2-444-2-4-4-2-20-20-42−2i32i322-20042i3−2i3-2-222200000−2i32i3002i3−2i30000000000000000000000000000000000000000
χ6344-44-2-444-2-4-4-2-20-20-422i3−2i322-2004−2i32i3-2-2222000002i3−2i300−2i32i30000000000000000000000000000000000000000
χ6444-4-244-4-24-2-2-4-40-202-40022-24-4200224-2-2-22-220000000004-4-22-2200000000000000000000000000000000
χ6544-4-244-4-24-2-2-4-40-202-40022-2-44200224-2-22-22-2000000000-442-22-200000000000000000000000000000000
χ6644-4-24-44-2422440-202-40022-200-200-2-2-42223−23−23230000000000023−23−232300000000000000000000000000000000
χ6744-4-24-44-2422440-202-40022-200-200-2-2-422−232323−2300000000000−232323−2300000000000000000000000000000000
χ6844-4-2-24-4-2-2-2-22201022−2i32i3-1-114-42−2i32i3-1-1-211-22-220i3−i300i3−i300-221-11-1−2i32i3i3−i3i3−i300000000000000000000000000
χ6944-4-2-24-4-2-2-2-22201022−2i32i3-1-11-442−2i32i3-1-1-2112-22-20i3−i300i3−i3002-2-11-112i3−2i3−i3i3−i3i300000000000000000000000000
χ7044-4-2-24-4-2-2-2-222010222i3−2i3-1-114-422i3−2i3-1-1-211-22-220−i3i300−i3i300-221-11-12i3−2i3−i3i3−i3i300000000000000000000000000
χ7144-4-2-24-4-2-2-2-222010222i3−2i3-1-11-4422i3−2i3-1-1-2112-22-20−i3i300−i3i3002-2-11-11−2i32i3i3−i3i3−i300000000000000000000000000
χ7244-4-2-2-44-2-222-2-201022−2i32i3-1-1100-22i3−2i3112-1-123−23−23230i3−i300−i3i30000−333−300−3i3i3i−3i00000000000000000000000000
χ7344-4-2-2-44-2-222-2-201022−2i32i3-1-1100-22i3−2i3112-1-1−232323−230i3−i300−i3i300003−3−33003i−3i−3i3i00000000000000000000000000
χ7444-4-2-2-44-2-222-2-2010222i3−2i3-1-1100-2−2i32i3112-1-123−23−23230−i3i300i3−i30000−333−3003i−3i−3i3i00000000000000000000000000
χ7544-4-2-2-44-2-222-2-2010222i3−2i3-1-1100-2−2i32i3112-1-1−232323−230−i3i300i3−i300003−3−3300−3i3i3i−3i00000000000000000000000000
χ768-808800-8-80000080000000-80000000000000000000000000000000000000000000000000000000000000
χ778-808-400-840043−430-4000000040000043−43000000000000000000000000000000000000000000000000000000
χ788-808-400-8400−43430-40000000400000−4343000000000000000000000000000000000000000000000000000000
χ798-80-48004-843−43000-4000000040000000043−43000000000000000000000000000000000000000000000000000
χ808-80-48004-8−4343000-40000000400000000−4343000000000000000000000000000000000000000000000000000
χ818-80-4-4004443−4343−4302000006-6-200000−23230−2323000000000000000000000000000000000000000000000000000
χ828-80-4-4004443−43−43430200000-66-20000023−230−2323000000000000000000000000000000000000000000000000000
χ838-80-4-40044−434343−430200000-66-200000−2323023−23000000000000000000000000000000000000000000000000000
χ848-80-4-40044−4343−434302000006-6-20000023−23023−23000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.