Finite Group Databasebeta

← Group #11778448

Character table — Group #11778448

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222244444444444444444444444488888888888888888888824242424242424242424242424242424242424242424242472727272
order122222336666662234466666666666666612121212466666612121212121212121212121212122244666688881212121224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-111-1-1
χ611111111111111-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-11-111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ711111111111111-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-1-1-1-111
χ811111111111111-1-11111111-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-1111111-1-1
χ922222222222222222-2-2222222222222222-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1022222222222222-2-22-2-22222-2-2-2-22222222-2-2-2-22-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ112222222-1222-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-1000000000000
χ122222222-1222-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100001111000000000000
χ132222222-1222-1-1-122-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-1-1-1-111-2-211111111110000−i3i3−i3i30000−i3i3−i3i3000000000000
χ142222222-1222-1-1-122-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-1-1-1-111-2-211111111110000i3−i3i3−i30000i3−i3i3−i3000000000000
χ152222222-1222-1-1-1-2-2-12222-1-11111-1-1-1-1-1-1-12222-2-2-21111-1-1-2-211-1-1-1-111112-22-2-1-1110000-1-111000000000000
χ162222222-1222-1-1-1-2-2-12222-1-11111-1-1-1-1-1-1-12222-2-2-21111-1-1-2-211-1-1-1-11111-22-2211-1-1000011-1-1000000000000
χ172222222-1222-1-1-1-2-2-1-2-222-1-11111-1-1-1-1-1-1-1-2-2-2-22-2-211111122-1-11111-1-1-1-10000−i3i3i3−i30000−i3i3i3−i3000000000000
χ182222222-1222-1-1-1-2-2-1-2-222-1-11111-1-1-1-1-1-1-1-2-2-2-22-2-211111122-1-11111-1-1-1-10000i3−i3−i3i30000i3−i3−i3i3000000000000
χ19222222-12-1-1-122222-122-1-1222222-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-10000
χ20222222-12-1-1-122222-122-1-1222222-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000-2-2-2-20000111111110000
χ21222222-12-1-1-122222-1-2-2-1-1222222-1-1-1-1-1-1-11111-2-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−30000
χ22222222-12-1-1-122222-1-2-2-1-1222222-1-1-1-1-1-1-11111-2-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−3330000
χ23222222-12-1-1-1222-2-2-122-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-21111112211-2-2-1-1-1-111110000000022-2-20000-1-1-1-111110000
χ24222222-12-1-1-1222-2-2-122-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-21111112211-2-2-1-1-1-1111100000000-2-22200001111-1-1-1-10000
χ25222222-12-1-1-1222-2-2-1-2-2-1-122-2-2-2-2-1-1-1-1-1-1-111112111111-2-2-1-1221111-1-1-1-1000000000000000033−3−3−3−3330000
χ26222222-12-1-1-1222-2-2-1-2-2-1-122-2-2-2-2-1-1-1-1-1-1-111112111111-2-2-1-1221111-1-1-1-10000000000000000−3−33333−3−30000
χ272222-2-2222222220022-2-2-2-2-200002-2-2-2-22222-2-200000002-2000022-2-20000020-20022000000-2-2000000000000
χ282222-2-2222222220022-2-2-2-2-200002-2-2-2-22222-2-200000002-2000022-2-200000-20200-2-200000022000000000000
χ292222-2-222222222002-22-2-2-2-200002-2-2-2-222-2-2220000000-220000-2-222000020-2022000000-2-200000000000000
χ302222-2-222222222002-22-2-2-2-200002-2-2-2-222-2-2220000000-220000-2-2220000-2020-2-20000002200000000000000
χ312222-2-22-1222-1-1-100-12-2-2-211−i3−i3i3i3-11111-1-122-2-2000−i3−i3i3i3-1100−i3i3-1-111−i3−i3i3i3020-2−i3i3-1-10000i3−i311000000000000
χ322222-2-22-1222-1-1-100-12-2-2-211−i3−i3i3i3-11111-1-122-2-2000−i3−i3i3i3-1100−i3i3-1-111−i3−i3i3i30-202i3−i3110000−i3i3-1-1000000000000
χ332222-2-22-1222-1-1-100-12-2-2-211i3i3−i3−i3-11111-1-122-2-2000i3i3−i3−i3-1100i3−i3-1-111i3i3−i3−i3020-2i3−i3-1-10000−i3i311000000000000
χ342222-2-22-1222-1-1-100-12-2-2-211i3i3−i3−i3-11111-1-122-2-2000i3i3−i3−i3-1100i3−i3-1-111i3i3−i3−i30-202−i3i3110000i3−i3-1-1000000000000
χ352222-2-22-1222-1-1-100-1-22-2-211−i3−i3i3i3-11111-1-1-2-222000−i3−i3i3i31-100i3−i311-1-1i3i3−i3−i320-20-1-1−i3i3000011i3−i3000000000000
χ362222-2-22-1222-1-1-100-1-22-2-211−i3−i3i3i3-11111-1-1-2-222000−i3−i3i3i31-100i3−i311-1-1i3i3−i3−i3-202011i3−i30000-1-1−i3i3000000000000
χ372222-2-22-1222-1-1-100-1-22-2-211i3i3−i3−i3-11111-1-1-2-222000i3i3−i3−i31-100−i3i311-1-1−i3−i3i3i320-20-1-1i3−i3000011−i3i3000000000000
χ382222-2-22-1222-1-1-100-1-22-2-211i3i3−i3−i3-11111-1-1-2-222000i3i3−i3−i31-100−i3i311-1-1−i3−i3i3i3-202011−i3i30000-1-1i3−i3000000000000
χ392-2-22-22222-2-2-2-222-22002-22-22-22-2222-2-2-2-2000002-22-22-200000000000000000000002−22−200002−22−22−22−20000
χ402-2-22-22222-2-2-2-222-22002-22-22-22-2222-2-2-2-2000002-22-22-20000000000000000000000−22−220000−22−22−22−220000
χ412-2-22-22222-2-2-2-22-222002-22-2-22-22222-2-2-2-200000-22-22-2200000000000000000000002−2−2200002−22−2−22−220000
χ422-2-22-22222-2-2-2-22-222002-22-2-22-22222-2-2-2-200000-22-22-220000000000000000000000−222−20000−22−222−22−20000
χ432-2-22-22-12-111-2-222-2-100-112-22-22-2-1-1-111113−33−30-11-11-11003−3003−33−33−33−3000000002−22−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ442-2-22-22-12-111-2-222-2-100-112-22-22-2-1-1-111113−33−30-11-11-11003−3003−33−33−33−300000000−22−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ452-2-22-22-12-111-2-222-2-100-112-22-22-2-1-1-11111−33−330-11-11-1100−3300−33−33−33−33000000002−22−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ462-2-22-22-12-111-2-222-2-100-112-22-22-2-1-1-11111−33−330-11-11-1100−3300−33−33−33−3300000000−22−220000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ472-2-22-22-12-111-2-22-22-100-112-2-22-22-1-1-111113−33−301-11-11-100−33003−33−3−33−33000000002−2−220000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ482-2-22-22-12-111-2-22-22-100-112-2-22-22-1-1-111113−33−301-11-11-100−33003−33−3−33−3300000000−222−20000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ492-2-22-22-12-111-2-22-22-100-112-2-22-22-1-1-11111−33−3301-11-11-1003−300−33−333−33−3000000002−2−220000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ502-2-22-22-12-111-2-22-22-100-112-2-22-22-1-1-11111−33−3301-11-11-1003−300−33−333−33−300000000−222−20000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ51444444-2-2-2-2-2-2-2-244144-2-2-2-2-2-2-2-21111111-2-2-2-24-2-21111-2-2-2-2-2-2111111110000000000000000000000000000
χ52444444-2-2-2-2-2-2-2-2441-4-4-2-2-2-2-2-2-2-211111112222-4-2-21111222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ53444444-2-2-2-2-2-2-2-2-4-4144-2-2-2-222221111111-2-2-2-2-422-1-1-1-1-2-222221111-1-1-1-10000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-2-4-41-4-4-2-2-2-2222211111112222422-1-1-1-122-2-2-2-2-1-1-1-111110000000000000000000000000000
χ554444-4-4-24-2-2-244400-24-422-4-40000-22222-2-2-2-22200000004-40000-2-22200000000000000000000000000000000
χ564444-4-4-24-2-2-244400-2-4422-4-40000-22222-2-222-2-20000000-44000022-2-200000000000000000000000000000000
χ574444-4-4-2-2-2-2-2-2-2-20014-42222−2i3−2i32i32i31-1-1-1-111-2-222000i3i3−i3−i3-2200−2i32i311-1-1i3i3−i3−i30000000000000000000000000000
χ584444-4-4-2-2-2-2-2-2-2-20014-422222i32i3−2i3−2i31-1-1-1-111-2-222000−i3−i3i3i3-22002i3−2i311-1-1−i3−i3i3i30000000000000000000000000000
χ594444-4-4-2-2-2-2-2-2-2-2001-442222−2i3−2i32i32i31-1-1-1-11122-2-2000i3i3−i3−i32-2002i3−2i3-1-111−i3−i3i3i30000000000000000000000000000
χ604444-4-4-2-2-2-2-2-2-2-2001-4422222i32i3−2i3−2i31-1-1-1-11122-2-2000−i3−i3i3i32-200−2i32i3-1-111i3i3−i3−i30000000000000000000000000000
χ6144-4-40044-44-44-4-40040000000000-400004-400000000000000000000000000000000000000000000000002i−2i00
χ6244-4-40044-44-44-4-40040000000000-400004-40000000000000000000000000000000000000000000000000−2i2i00
χ634-44-40044-4-44-44-40040000000000-40000-440000000000000000000000000000000000000000000000000002i−2i
χ644-44-40044-4-44-44-40040000000000-40000-44000000000000000000000000000000000000000000000000000−2i2i
χ654-4-444-4444-4-4-4-4400400-44-4400004-4-444-4-400000000000000000000000000000000000000000000000000000
χ664-4-444-44-24-4-422-200-200-442-2−2i32i32i3−2i3-222-2-2220000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ674-4-444-44-24-4-422-200-200-442-22i3−2i3−2i32i3-222-2-22200000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ684-4-444-4-24-222-4-4400-2002-2-440000-222-2-22223−23−2323000000000000023−23−232300000000000000000000000000000000
χ694-4-444-4-24-222-4-4400-2002-2-440000-222-2-222−232323−230000000000000−232323−2300000000000000000000000000000000
χ704-4-444-4-2-2-22222-2001002-22-2−2i32i32i3−2i31-1-111-1-123−23−2323000i3−i3−i3i3000000−333−3−3i3i3i−3i0000000000000000000000000000
χ714-4-444-4-2-2-22222-2001002-22-2−2i32i32i3−2i31-1-111-1-1−232323−23000i3−i3−i3i30000003−3−333i−3i−3i3i0000000000000000000000000000
χ724-4-444-4-2-2-22222-2001002-22-22i3−2i3−2i32i31-1-111-1-123−23−2323000−i3i3i3−i3000000−333−33i−3i−3i3i0000000000000000000000000000
χ734-4-444-4-2-2-22222-2001002-22-22i3−2i3−2i32i31-1-111-1-1−232323−23000−i3i3i3−i30000003−3−33−3i3i3i−3i0000000000000000000000000000
χ744-4-44-444-24-4-422-24-4-2004-4-22-22-22-2-2-22222000004-4-22-22000000000000000000000000000000000000000000
χ754-4-44-444-24-4-422-2-44-2004-4-222-22-2-2-2-2222200000-442-22-2000000000000000000000000000000000000000000
χ764-4-44-44-2-2-22222-24-4100-22-22-22-22111-1-1-1-123−2323−230-221-11-10023−2300−33−33−33−330000000000000000000000000000
χ774-4-44-44-2-2-22222-24-4100-22-22-22-22111-1-1-1-1−2323−23230-221-11-100−2323003−33−33−33−30000000000000000000000000000
χ784-4-44-44-2-2-22222-2-44100-22-222-22-2111-1-1-1-123−2323−2302-2-11-1100−232300−33−333−33−30000000000000000000000000000
χ794-4-44-44-2-2-22222-2-44100-22-222-22-2111-1-1-1-1−2323−232302-2-11-110023−23003−33−3−33−330000000000000000000000000000
χ8088-8-8008-4-88-8-44400-4000000000040000-4400000000000000000000000000000000000000000000000000000
χ8188-8-800-484-448-8-800-4000000000040000-4400000000000000000000000000000000000000000000000000000
χ8288-8-800-4-44-44-4440020000000000-26-66-62-200000000000000000000000000000000000000000000000000000
χ8388-8-800-4-44-44-4440020000000000-2-66-662-200000000000000000000000000000000000000000000000000000
χ848-88-8008-4-8-884-4400-40000000000400004-400000000000000000000000000000000000000000000000000000
χ858-88-800-4844-4-88-800-40000000000400004-400000000000000000000000000000000000000000000000000000
χ868-88-800-4-444-44-440020000000000-26-6-66-2200000000000000000000000000000000000000000000000000000
χ878-88-800-4-444-44-440020000000000-2-666-6-2200000000000000000000000000000000000000000000000000000

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