Finite Group Databasebeta

← Group #11780201

Character table — Group #11780201

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order122233444466666612121212344466612121212121212121212121212121212412121212121212121212121212121212121212226666888824242424242424244448812121212121224242424884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-11111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ5111111111111111111111-1-11111111111-1-1-1-1111111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-11111111111-1-1-1-1111111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11
χ7111111111111111111111-1-11111111111-1-1-1-1111111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-11111-1-1-1-1-1-11
χ8111111111111111111111-1-11111111111-1-1-1-1111111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1
χ92222222-22-22222222222200-222222-2-2-2-200002222-2-20-2000000-2-2-2-200000000222222000000000000-20000-2-200000000000
χ102222222-22-22222222222200-222222-2-2-2-200002222-2-20-2000000-2-2-2-200000000-2-2-2-2-2-2000000000000200002200000000000
χ11222222-22-22222222-2-2-2-2222-2222-2-222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2-2-2000000000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2-2-2222-2-22222-2-2-2-2-2-2-2-2-2-22-2-2-2222222-2-2-2-2-2-22222000000000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-20000-2-2-2-22202000000-2-2220000000000000000000000000002-2000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-20000-2-2-2-22202000000-2-222000000000000000000000000000-220000-2-2220000000
χ1522222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000022200-1-1-1-1-1-10000000
χ1622222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000000000-2-2-2001111110000000
χ1722222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-11111-1-1-1-122-2-1-2-2-2-211-1-1-1-11111111122-1-1-1-10000000000002-2-200-1-111110000000
χ1822222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-11111-1-1-1-122-2-1-2-2-2-211-1-1-1-111111111-2-21111000000000000-2220011-1-1-1-10000000
χ1922222-12-22-22-122-1-12222-100-2-1-1-1-1-1-2-211−i3−i3i3i3-1-1-1-1-2-2010000−i3i31111−i3−i3i3i3−i3−i3i3i322-1-1-1-1000000000000-2000011−i3i3−i3i30000000
χ2022222-12-22-22-122-1-12222-100-2-1-1-1-1-1-2-211−i3−i3i3i3-1-1-1-1-2-2010000−i3i31111−i3−i3i3i3−i3−i3i3i3-2-2111100000000000020000-1-1i3−i3i3−i30000000
χ2122222-12-22-22-122-1-12222-100-2-1-1-1-1-1-2-211i3i3−i3−i3-1-1-1-1-2-2010000i3−i31111i3i3−i3−i3i3i3−i3−i322-1-1-1-1000000000000-2000011i3−i3i3−i30000000
χ2222222-12-22-22-122-1-12222-100-2-1-1-1-1-1-2-211i3i3−i3−i3-1-1-1-1-2-2010000i3−i31111i3i3−i3−i3i3i3−i3−i3-2-2111100000000000020000-1-1−i3i3−i3i30000000
χ2322222-1-22-222-122-1-1-2-2-2-2-122-2-1-1-11122-1-1-1-1-1-11111-2-2-2122-2-211-1-111-1-1-1-1111100−i3−i3i3i300000000000000000−i3i3−i3i3i3−i30000000
χ2422222-1-22-222-122-1-1-2-2-2-2-122-2-1-1-11122-1-1-1-1-1-11111-2-2-2122-2-211-1-111-1-1-1-1111100i3i3−i3−i300000000000000000i3−i3i3−i3−i3i30000000
χ2522222-1-22-222-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-1-111111111-2-221-2-222-1-1-1-1111111-1-1-1-100−i3−i3i3i300000000000000000−i3i3i3−i3−i3i30000000
χ2622222-1-22-222-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-1-111111111-2-221-2-222-1-1-1-1111111-1-1-1-100i3i3−i3−i300000000000000000i3−i3−i3i3i3−i30000000
χ2722222-1-2-2-2-22-122-1-1-2-2-2-2-1002-1-1-111-2-211−i3−i3i3i31111220-10000i3−i311-1-1−i3−i3i3i3i3i3−i3−i300−i3−i3i3i300000000000002-200i3−i3-1-1110000000
χ2822222-1-2-2-2-22-122-1-1-2-2-2-2-1002-1-1-111-2-211−i3−i3i3i31111220-10000i3−i311-1-1−i3−i3i3i3i3i3−i3−i300i3i3−i3−i30000000000000-2200−i3i311-1-10000000
χ2922222-1-2-2-2-22-122-1-1-2-2-2-2-1002-1-1-111-2-211i3i3−i3−i31111220-10000−i3i311-1-1i3i3−i3−i3−i3−i3i3i300−i3−i3i3i30000000000000-2200i3−i311-1-10000000
χ3022222-1-2-2-2-22-122-1-1-2-2-2-2-1002-1-1-111-2-211i3i3−i3−i31111220-10000−i3i311-1-1i3i3−i3−i3−i3−i3i3i300i3i3−i3−i300000000000002-200−i3i3-1-1110000000
χ312222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-1222222-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000002222-1-1-1-1-1-1-1-100022000000-1-1-1-1000
χ322222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-1222222-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-211111111000-2-20000001111000
χ332222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-122-2-2-2-2-1-1-1-1-1-1-221111-2-2-1-1-1-1111111110000002222-1-1-1-1-1-1-1-1000-2-20000001111000
χ342222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-122-2-2-2-2-1-1-1-1-1-1-221111-2-2-1-1-1-111111111000000-2-2-2-21111111100022000000-1-1-1-1000
χ352222-12-22-22-12-1-1221111-122-2-1-1-1-2-2-1-1222222111111-2-2-1-111-2-2-1-111-1-1-1-1111100000000003333−3−3−3−30000000000033−3−3000
χ362222-12-22-22-12-1-1221111-122-2-1-1-1-2-2-1-1222222111111-2-2-1-111-2-2-1-111-1-1-1-111110000000000−3−3−3−3333300000000000−3−333000
χ372222-12-22-22-12-1-1221111-1-2-2-2-1-1-1-2-2-1-122-2-2-2-21111112-211-1-122-1-1111111-1-1-1-100000000003333−3−3−3−300000000000−3−333000
χ382222-12-22-22-12-1-1221111-1-2-2-2-1-1-1-2-2-1-122-2-2-2-21111112-211-1-122-1-1111111-1-1-1-10000000000−3−3−3−333330000000000033−3−3000
χ3922-2-22220-2022-2-2-2-222-2-220002-2-22-20000000022-2-200000000000000000000002-22-22-222−2−222−2−222−2−20000000000000002−20
χ4022-2-22220-2022-2-2-2-222-2-220002-2-22-20000000022-2-200000000000000000000002-22-22-2−2−222−2−222−2−222000000000000000−220
χ4122-2-22220-2022-2-2-2-222-2-220002-2-22-20000000022-2-20000000000000000000000-22-22-2222−2−222−2−222−2−2000000000000000−220
χ4222-2-22220-2022-2-2-2-222-2-220002-2-22-20000000022-2-20000000000000000000000-22-22-22−2−222−2−222−2−2220000000000000002−20
χ432-2-22220-202-2-22-2-22000022-20-22-2002-22-22-22-2000000002-200002-2002-22-200000000002−22−22−22−22−22−20002−20000002−22−2000
χ442-2-22220-202-2-22-2-22000022-20-22-2002-22-22-22-2000000002-200002-2002-22-20000000000−22−22−22−22−22−22000−22000000−22−22000
χ452-2-22220-202-2-22-2-2200002-220-22-2002-22-2-22-2200000000-2200002-200-22-2200000000002−22−22−22−22−22−2000−22000000−22−22000
χ462-2-22220-202-2-22-2-2200002-220-22-2002-22-2-22-2200000000-2200002-200-22-220000000000−22−22−22−22−22−220002−20000002−22−2000
χ472-2-22-120-2021-2-11-223−33−3-12-201-1100-112-22-22-23−33−33−300-113−300-113−3-11-113−33−30000002−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230002−2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000
χ482-2-22-120-2021-2-11-223−33−3-12-201-1100-112-22-22-23−33−33−300-113−300-113−3-11-113−33−3000000−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000−22000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000
χ492-2-22-120-2021-2-11-223−33−3-1-2201-1100-112-2-22-223−33−33−3001-1−3300-113−31-11-1−33−330000002−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000−22000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000
χ502-2-22-120-2021-2-11-223−33−3-1-2201-1100-112-2-22-223−33−33−3001-1−3300-113−31-11-1−33−33000000−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230002−2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000
χ512-2-22-120-2021-2-11-22−33−33-12-201-1100-112-22-22-2−33−33−3300-11−3300-11−33-11-11−33−330000002−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70002−2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000
χ522-2-22-120-2021-2-11-22−33−33-12-201-1100-112-22-22-2−33−33−3300-11−3300-11−33-11-11−33−33000000−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000−22000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000
χ532-2-22-120-2021-2-11-22−33−33-1-2201-1100-112-2-22-22−33−33−33001-13−300-11−331-11-13−33−30000002−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000−22000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000
χ542-2-22-120-2021-2-11-22−33−33-1-2201-1100-112-2-22-22−33−33−33001-13−300-11−331-11-13−33−3000000−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70002−2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000
χ554444-244-44-4-24-2-244-2-2-2-2-200-4-2-2-24422-4-40000-2-2-2-2220-4000000222200000000000000000000000000000000000000000000
χ564444-24-4-4-4-4-24-2-2442222-2004-2-2-2-4-422-4-400002222-2-20400000022-2-200000000000000000000000000000000000000000000
χ574444-2-24444-2-2-2-2-2-2-2-2-2-21444111-2-2-2-2-2-2-2-2-2-21111-2-24-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ584444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-2-2-2-2-222221111-2-2-4-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-4111-2-22222−2i3−2i32i32i3111122020000−2i32i3-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ604444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-4111-2-222222i32i3−2i3−2i31111220200002i3−2i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ614444-2-2-44-44-2-2-2-2-2-22222144-411122-2-2-2-2-2-2-2-2-1-1-1-122-42-2-2222211-1-11111-1-1-1-1000000000000000000000000000000000000
χ624444-2-2-44-44-2-2-2-2-2-222221-4-4-411122-2-2-2-22222-1-1-1-1224222-2-2-2-211-1-1-1-1-1-11111000000000000000000000000000000000000
χ634444-2-2-4-4-4-4-2-2-2-2-2-222221004111222222−2i3−2i32i32i3-1-1-1-1-2-20-200002i3−2i3-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000000000
χ644444-2-2-4-4-4-4-2-2-2-2-2-2222210041112222222i32i3−2i3−2i3-1-1-1-1-2-20-20000−2i32i3-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000
χ6544-4-444-404044-4-4-4-4-4-44440004-4-4-4400000000-4-4440000000000000000000000000000000000000000000000000000000000
χ6644-4-44-240-404-2-4-42244-4-4-2000-222-2200000000-2-22200000000000000000000004-4-22-22000000000000000000000000000000
χ6744-4-44-240-404-2-4-42244-4-4-2000-222-2200000000-2-2220000000000000000000000-442-22-2000000000000000000000000000000
χ6844-4-44-2-40404-2-4-422-4-444-2000-2222-20000000022-2-2000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6944-4-44-2-40404-2-4-422-4-444-2000-2222-20000000022-2-20000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ7044-4-4-2440-40-2422-4-4-2-222-2000-2224-400000000-2-22200000000000000000000000000002222−22−22−2−222−2−222000000000000000000
χ7144-4-4-2440-40-2422-4-4-2-222-2000-2224-400000000-2-2220000000000000000000000000000−22−22222222−2−222−2−2000000000000000000
χ7244-4-4-24-4040-2422-4-422-2-2-2000-222-440000000022-2-20000000000000000000000000000000066−6−6−6−666000000000000000000
χ7344-4-4-24-4040-2422-4-422-2-2-2000-222-440000000022-2-200000000000000000000000000000000−6−66666−6−6000000000000000000
χ744-44-4440000-4-4-444-400004000-4-440000000000000000000000000000000000000000002-2-222-2-222-2-22000000000000000000
χ754-44-4440000-4-4-444-400004000-4-44000000000000000000000000000000000000000000-222-2-222-2-222-2000000000000000000
χ764-44-4-2400002-42-24-423−23−2323-200022-2000000000023−23−232300000000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000
χ774-44-4-2400002-42-24-423−23−2323-200022-2000000000023−23−23230000000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000
χ784-44-4-2400002-42-24-4−232323−23-200022-20000000000−232323−2300000000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000
χ794-44-4-2400002-42-24-4−232323−23-200022-20000000000−232323−230000000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000
χ804-4-4444040-4-4-44-4-4400004000-44-400-44-44000000000000000000-440000000000000000000000000000000000000000000000
χ814-4-444-2040-4-424-42-20000-20002-2200-442-2−2i32i32i3−2i3000000000000002-200−2i32i32i3−2i30000000000000000000000000000000000000000
χ824-4-444-2040-4-424-42-20000-20002-2200-442-22i3−2i3−2i32i3000000000000002-2002i3−2i3−2i32i30000000000000000000000000000000000000000
χ834-4-444-20-404-424-42-20000-24-402-22004-4-22-22-22000000004-40000-2200-22-220000000000000000000000000000000000000000
χ844-4-444-20-404-424-42-20000-2-4402-22004-4-222-22-200000000-440000-22002-22-20000000000000000000000000000000000000000
χ854-4-44-24040-42-4-22-4423−2323−23-20002-22002-2-44000023−2323−23−2323000000002-2−232300000000000000000000000000000000000000000000
χ864-4-44-24040-42-4-22-44−2323−2323-20002-22002-2-440000−2323−232323−23000000002-223−2300000000000000000000000000000000000000000000
χ874-4-44-2-2040-422-222-223−2323−231000-11-1002-22-2−2i32i32i3−2i3−33−33−232300000000-113−3i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000000000
χ884-4-44-2-2040-422-222-223−2323−231000-11-1002-22-22i3−2i3−2i32i3−33−33−232300000000-113−3−i3i3i3−i33i−3i−3i3i000000000000000000000000000000000000
χ894-4-44-2-2040-422-222-2−2323−23231000-11-1002-22-2−2i32i32i3−2i33−33−323−2300000000-11−33i3−i3−i3i33i−3i−3i3i000000000000000000000000000000000000
χ904-4-44-2-2040-422-222-2−2323−23231000-11-1002-22-22i3−2i3−2i32i33−33−323−2300000000-11−33−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000000000
χ914-4-44-2-20-40422-222-223−2323−2314-40-11-100-22-22-22-22−33−3323−2300-2223−23001-1−331-11-1−33−33000000000000000000000000000000000000
χ924-4-44-2-20-40422-222-223−2323−231-440-11-100-22-222-22-2−33−3323−23002-2−2323001-1−33-11-113−33−3000000000000000000000000000000000000
χ934-4-44-2-20-40422-222-2−2323−232314-40-11-100-22-22-22-223−33−3−232300-22−2323001-13−31-11-13−33−3000000000000000000000000000000000000
χ944-4-44-2-20-40422-222-2−2323−23231-440-11-100-22-222-22-23−33−3−2323002-223−23001-13−3-11-11−33−33000000000000000000000000000000000000
χ9588-8-8-4-480-80-4-44444-4-44420002-2-2-440000000022-2-20000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-8080-4-4444444-4-420002-2-24-400000000-2-2220000000000000000000000000000000000000000000000000000000000
χ978-88-88-40000-84-88-440000-400044-4000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-40000444-4-4443−43−43432000-2-220000000000−232323−230000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-40000444-4-44−434343−432000-2-22000000000023−23−23230000000000000000000000000000000000000000000000000000000000

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