Finite Group Databasebeta

← Group #11772782

Character table — Group #11772782

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112224444448888888888881616161624242424484811222444444888888888888161616162424242448481122244444488888888888816161616242424244848
order12236444612122444661212121212128122424888888366361212126121261212126612121212121224122424242424242424366361212126121261212126612121212121224122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1
χ311111111111-11-11-1-111-1-111-11-1-11111-1-111111111111-11-11-1-111-1-111-11-1-11111-1-111111111111-11-11-1-111-1-111-11-1-11111-1-1
χ411111111111-11-11-1-111-1-111-11-1-1-1-1-1-11111111111111-11-11-1-111-1-111-11-1-1-1-1-1-11111111111111-11-11-1-111-1-111-11-1-1-1-1-1-111
χ511111-11-1111111-1111111-1-1-1-1-1-1ii−i−ii−i11111-11-1111111-1111111-1-1-1-1-1-1ii−i−ii−i11111-11-1111111-1111111-1-1-1-1-1-1ii−i−ii−i
χ611111-11-1111111-1111111-1-1-1-1-1-1−i−iii−ii11111-11-1111111-1111111-1-1-1-1-1-1−i−iii−ii11111-11-1111111-1111111-1-1-1-1-1-1−i−iii−ii
χ711111-11-1111-11-1-1-1-111-1-1-1-11-111ii−i−i−ii11111-11-1111-11-1-1-1-111-1-1-1-11-111ii−i−i−ii11111-11-1111-11-1-1-1-111-1-1-1-11-111ii−i−i−ii
χ811111-11-1111-11-1-1-1-111-1-1-1-11-111−i−iiii−i11111-11-1111-11-1-1-1-111-1-1-1-11-111−i−iiii−i11111-11-1111-11-1-1-1-111-1-1-1-11-111−i−iiii−i
χ9222222222220-20-200-2-200220-200000000222222222220-20-200-2-200220-200000000222222222220-20-200-2-200220-200000000
χ1022222-22-22220-20200-2-200-2-2020000000022222-22-22220-20200-2-200-2-2020000000022222-22-22220-20200-2-200-2-20200000000
χ11222-1-1222-1-1-10-20-2−i3i311−i3i3-1-101−i3i3000000222-1-1222-1-1-10-20-2−i3i311−i3i3-1-101−i3i3000000222-1-1222-1-1-10-20-2−i3i311−i3i3-1-101−i3i3000000
χ12222-1-1222-1-1-10-20-2i3−i311i3−i3-1-101i3−i3000000222-1-1222-1-1-10-20-2i3−i311i3−i3-1-101i3−i3000000222-1-1222-1-1-10-20-2i3−i311i3−i3-1-101i3−i3000000
χ13222-1-1222-1-1-12222-1-1-1-1-1-1-1-12-1-1-1000000222-1-1222-1-1-12222-1-1-1-1-1-1-1-12-1-1-1000000222-1-1222-1-1-12222-1-1-1-1-1-1-1-12-1-1-1000000
χ14222-1-1222-1-1-1-22-2211-1-111-1-1-2-111000000222-1-1222-1-1-1-22-2211-1-111-1-1-2-111000000222-1-1222-1-1-1-22-2211-1-111-1-1-2-111000000
χ15222-1-1-22-2-1-1-10-202−i3i311−i3i3110-1i3−i3000000222-1-1-22-2-1-1-10-202−i3i311−i3i3110-1i3−i3000000222-1-1-22-2-1-1-10-202−i3i311−i3i3110-1i3−i3000000
χ16222-1-1-22-2-1-1-10-202i3−i311i3−i3110-1−i3i3000000222-1-1-22-2-1-1-10-202i3−i311i3−i3110-1−i3i3000000222-1-1-22-2-1-1-10-202i3−i311i3−i3110-1−i3i3000000
χ17222-1-1-22-2-1-1-1222-2-1-1-1-1-1-111-2111000000222-1-1-22-2-1-1-1222-2-1-1-1-1-1-111-2111000000222-1-1-22-2-1-1-1222-2-1-1-1-1-1-111-2111000000
χ18222-1-1-22-2-1-1-1-22-2-211-1-1111121-1-1000000222-1-1-22-2-1-1-1-22-2-211-1-1111121-1-1000000222-1-1-22-2-1-1-1-22-2-211-1-1111121-1-1000000
χ19444440-404-4-40000000000000000000000444440-404-4-40000000000000000000000444440-404-4-40000000000000000000000
χ20444-2-20-40-222000000−2i32i300000000000000444-2-20-40-222000000−2i32i300000000000000444-2-20-40-222000000−2i32i300000000000000
χ21444-2-20-40-2220000002i3−2i300000000000000444-2-20-40-2220000002i3−2i300000000000000444-2-20-40-2220000002i3−2i300000000000000
χ2244-444000-40020-202200-2-200000000000044-444000-40020-202200-2-200000000000044-444000-40020-202200-2-2000000000000
χ2344-444000-400-2020-2-2002200000000000044-444000-400-2020-2-2002200000000000044-444000-400-2020-2-20022000000000000
χ2444-4-2-20002−2i32i320-20−1−i3−1+i3001+i31−i300000000000044-4-2-20002−2i32i320-20−1−i3−1+i3001+i31−i300000000000044-4-2-20002−2i32i320-20−1−i3−1+i3001+i31−i3000000000000
χ2544-4-2-20002−2i32i3-20201+i31−i300−1−i3−1+i300000000000044-4-2-20002−2i32i3-20201+i31−i300−1−i3−1+i300000000000044-4-2-20002−2i32i3-20201+i31−i300−1−i3−1+i3000000000000
χ2644-4-2-200022i3−2i320-20−1+i3−1−i3001−i31+i300000000000044-4-2-200022i3−2i320-20−1+i3−1−i3001−i31+i300000000000044-4-2-200022i3−2i320-20−1+i3−1−i3001−i31+i3000000000000
χ2744-4-2-200022i3−2i3-20201−i31+i300−1+i3−1−i300000000000044-4-2-200022i3−2i3-20201−i31+i300−1+i3−1−i300000000000044-4-2-200022i3−2i3-20201−i31+i300−1+i3−1−i3000000000000
χ284-404-420-200000000000002-200002−22−2004-404-420-200000000000002-200002−22−2004-404-420-200000000000002-200002−22−200
χ294-404-420-200000000000002-20000−22−22004-404-420-200000000000002-20000−22−22004-404-420-200000000000002-20000−22−2200
χ304-404-4-2020000000000000-220000−i2i2i2−i2004-404-4-2020000000000000-220000−i2i2i2−i2004-404-4-2020000000000000-220000−i2i2i2−i200
χ314-404-4-2020000000000000-220000i2−i2−i2i2004-404-4-2020000000000000-220000i2−i2−i2i2004-404-4-2020000000000000-220000i2−i2−i2i200
χ328-80-4440-40000000000000-2200000000008-80-4440-40000000000000-2200000000008-80-4440-40000000000000-220000000000
χ338-80-44-40400000000000002-200000000008-80-44-40400000000000002-200000000008-80-44-40400000000000002-20000000000
χ34111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ35111111111111111111111111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ3611111111111-11-11-1-111-1-111-11-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ3711111111111-11-11-1-111-1-111-11-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ3811111-11-1111111-1111111-1-1-1-1-1-1ii−i−ii−i−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32ζ14ζ14−ζ14−ζ14ζ14−ζ14−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32ζ22ζ22−ζ22−ζ22ζ22−ζ22
χ3911111-11-1111111-1111111-1-1-1-1-1-1−i−iii−ii−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−ζ14−ζ14ζ14ζ14−ζ14ζ14−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−ζ22−ζ22ζ22ζ22−ζ22ζ22
χ4011111-11-1111-11-1-1-1-111-1-1-1-11-111ii−i−i−ii−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32ζ14ζ14−ζ14−ζ14−ζ14ζ14−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32ζ22ζ22−ζ22−ζ22−ζ22ζ22
χ4111111-11-1111-11-1-1-1-111-1-1-1-11-111−i−iiii−i−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i32−ζ14−ζ14ζ14ζ14ζ14−ζ14−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−ζ22−ζ22ζ22ζ22ζ22−ζ22
χ42222222222220-20-200-2-200220-200000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i301−i301−i3001−i31−i300−1+i3−1+i301−i300000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i301+i301+i3001+i31+i300−1−i3−1−i301+i300000000
χ4322222-22-22220-20200-2-200-2-20200000000−1+i3−1+i3−1+i3−1+i3−1+i31−i3−1+i31−i3−1+i3−1+i3−1+i301−i30−1+i3001−i31−i3001−i31−i30−1+i300000000−1−i3−1−i3−1−i3−1−i3−1−i31+i3−1−i31+i3−1−i3−1−i3−1−i301+i30−1−i3001+i31+i3001+i31+i30−1−i300000000
χ44222-1-1222-1-1-10-20-2−i3i311−i3i3-1-101−i3i3000000−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i31−i321−i321−i3201−i301−i33+i32−3−i32−1+i32−1+i323+i32−3−i321−i321−i320−1+i323+i32−3−i32000000−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i31+i321+i321+i3201+i301+i3−3+i323−i32−1−i32−1−i32−3+i323−i321+i321+i320−1−i32−3+i323−i32000000
χ45222-1-1222-1-1-10-20-2i3−i311i3−i3-1-101i3−i3000000−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i31−i321−i321−i3201−i301−i3−3−i323+i32−1+i32−1+i32−3−i323+i321−i321−i320−1+i32−3−i323+i32000000−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i31+i321+i321+i3201+i301+i33−i32−3+i32−1−i32−1−i323−i32−3+i321+i321+i320−1−i323−i32−3+i32000000
χ46222-1-1222-1-1-12222-1-1-1-1-1-1-1-12-1-1-1000000−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i31−i321−i321−i32000000−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i31+i321+i321+i32000000
χ47222-1-1222-1-1-1-22-2211-1-111-1-1-2-111000000−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i3−1+i31−i321−i321−i321−i3−1+i31−i3−1+i3−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i31−i32−1+i32−1+i32000000−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i3−1−i31+i321+i321+i321+i3−1−i31+i3−1−i3−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i31+i32−1−i32−1−i32000000
χ48222-1-1-22-2-1-1-10-202−i3i311−i3i3110-1i3−i3000000−1+i3−1+i3−1+i31−i321−i321−i3−1+i31−i31−i321−i321−i3201−i30−1+i33+i32−3−i32−1+i32−1+i323+i32−3−i32−1+i32−1+i3201−i32−3−i323+i32000000−1−i3−1−i3−1−i31+i321+i321+i3−1−i31+i31+i321+i321+i3201+i30−1−i3−3+i323−i32−1−i32−1−i32−3+i323−i32−1−i32−1−i3201+i323−i32−3+i32000000
χ49222-1-1-22-2-1-1-10-202i3−i311i3−i3110-1−i3i3000000−1+i3−1+i3−1+i31−i321−i321−i3−1+i31−i31−i321−i321−i3201−i30−1+i3−3−i323+i32−1+i32−1+i32−3−i323+i32−1+i32−1+i3201−i323+i32−3−i32000000−1−i3−1−i3−1−i31+i321+i321+i3−1−i31+i31+i321+i321+i3201+i30−1−i33−i32−3+i32−1−i32−1−i323−i32−3+i32−1−i32−1−i3201+i32−3+i323−i32000000
χ50222-1-1-22-2-1-1-1222-2-1-1-1-1-1-111-2111000000−1+i3−1+i3−1+i31−i321−i321−i3−1+i31−i31−i321−i321−i32−1+i3−1+i3−1+i31−i31−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i3−1+i32−1+i32−1+i32000000−1−i3−1−i3−1−i31+i321+i321+i3−1−i31+i31+i321+i321+i32−1−i3−1−i3−1−i31+i31+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i3−1−i32−1−i32−1−i32000000
χ51222-1-1-22-2-1-1-1-22-2-211-1-1111121-1-1000000−1+i3−1+i3−1+i31−i321−i321−i3−1+i31−i31−i321−i321−i321−i3−1+i31−i31−i3−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i3−1+i321−i321−i32000000−1−i3−1−i3−1−i31+i321+i321+i3−1−i31+i31+i321+i321+i321+i3−1−i31+i31+i3−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i3−1−i321+i321+i32000000
χ52444440-404-4-40000000000000000000000−2+2i3−2+2i3−2+2i3−2+2i3−2+2i302−2i30−2+2i32−2i32−2i30000000000000000000000−2−2i3−2−2i3−2−2i3−2−2i3−2−2i302+2i30−2−2i32+2i32+2i30000000000000000000000
χ53444-2-20-40-222000000−2i32i300000000000000−2+2i3−2+2i3−2+2i31−i31−i302−2i301−i3−1+i3−1+i30000003+i3−3−i300000000000000−2−2i3−2−2i3−2−2i31+i31+i302+2i301+i3−1−i3−1−i3000000−3+i33−i300000000000000
χ54444-2-20-40-2220000002i3−2i300000000000000−2+2i3−2+2i3−2+2i31−i31−i302−2i301−i3−1+i3−1+i3000000−3−i33+i300000000000000−2−2i3−2−2i3−2−2i31+i31+i302+2i301+i3−1−i3−1−i30000003−i3−3+i300000000000000
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χ9344-4-2-200022i3−2i3-20201−i31+i300−1+i3−1−i3000000000000−2−2i3−2−2i32+2i31+i31+i3000−1−i33−i3−3+i31+i30−1−i30-21−i3002−1+i3000000000000−2+2i3−2+2i32−2i31−i31−i3000−1+i3−3−i33+i31−i30−1+i301+i3-200−1−i32000000000000
χ944-404-420-200000000000002-200002−22−200−2−2i32+2i30−2−2i32+2i3−1−i301+i30000000000000−1−i31+i30000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ1300−2+2i32−2i30−2+2i32−2i3−1+i301−i30000000000000−1+i31−i30000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ2300
χ954-404-420-200000000000002-20000−22−2200−2−2i32+2i30−2−2i32+2i3−1−i301+i30000000000000−1−i31+i30000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ1300−2+2i32−2i30−2+2i32−2i3−1+i301−i30000000000000−1+i31−i30000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ2300
χ964-404-4-2020000000000000-220000−i2i2i2−i200−2−2i32+2i30−2−2i32+2i31+i30−1−i300000000000001+i3−1−i30000ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ1300−2+2i32−2i30−2+2i32−2i31−i30−1+i300000000000001−i3−1+i30000ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ2300
χ974-404-4-2020000000000000-220000i2−i2−i2i200−2−2i32+2i30−2−2i32+2i31+i30−1−i300000000000001+i3−1−i30000−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ1300−2+2i32−2i30−2+2i32−2i31−i30−1+i300000000000001−i3−1+i30000−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ2300
χ988-80-4440-40000000000000-220000000000−4−4i34+4i302+2i3−2−2i3−2−2i302+2i300000000000001+i3−1−i30000000000−4+4i34−4i302−2i3−2+2i3−2+2i302−2i300000000000001−i3−1+i30000000000
χ998-80-44-40400000000000002-20000000000−4−4i34+4i302+2i3−2−2i32+2i30−2−2i30000000000000−1−i31+i30000000000−4+4i34−4i302−2i3−2+2i32−2i30−2+2i30000000000000−1+i31−i30000000000

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