Finite Group Databasebeta

← Group #11724297

Character table — Group #11724297

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112444488991212121218181818182424242411244448899121212121818181818242424241124444889912121212181818181824242424
order122336666222244244446612123663366666666121261212121266121236633666666661212612121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-11-11-1-1-1-11-11-1111111111111-11-11-1-1-1-11-11-1111111111111-11-11-1-1-1-11-11-1
χ311111111111-11-111-1-1-1-1-11-1111111111111-11-111-1-1-1-1-11-1111111111111-11-111-1-1-1-1-11-11
χ411111111111-1-1-1-111111-1-1-1-111111111111-1-1-1-111111-1-1-1-111111111111-1-1-1-111111-1-1-1-1
χ511-11111-1-11111-1-1-111-1-111-1-111-11111-1-11111-1-1-111-1-111-1-111-11111-1-11111-1-1-111-1-111-1-1
χ611-11111-1-1111-1-11-1-1-1111-1-1111-11111-1-1111-1-11-1-1-1111-1-1111-11111-1-1111-1-11-1-1-1111-1-11
χ711-11111-1-111-111-1-1-1-111-111-111-11111-1-111-111-1-1-1-111-111-111-11111-1-111-111-1-1-1-111-111-1
χ811-11111-1-111-1-111-111-1-1-1-11111-11111-1-111-1-111-111-1-1-1-11111-11111-1-111-1-111-111-1-1-1-111
χ9222222222-2-20000-200000000222222222-2-20000-200000000222222222-2-20000-200000000
χ1022-22222-2-2-2-2000020000000022-22222-2-2-2-2000020000000022-22222-2-2-2-20000200000000
χ112-2022-2-2002-200000002i−2i00002-2022-2-2002-200000002i−2i00002-2022-2-2002-200000002i−2i0000
χ122-2022-2-2002-20000000−2i2i00002-2022-2-2002-20000000−2i2i00002-2022-2-2002-20000000−2i2i0000
χ132-2022-2-200-22000002-20000002-2022-2-200-22000002-20000002-2022-2-200-22000002-2000000
χ142-2022-2-200-2200000-220000002-2022-2-200-2200000-220000002-2022-2-200-2200000-22000000
χ154441-21-21-2000202000000-10-14441-21-21-2000202000000-10-14441-21-21-2000202000000-10-1
χ164441-21-21-2000-20-20000001014441-21-21-2000-20-20000001014441-21-21-2000-20-2000000101
χ17444-21-21-2100202000000-10-10444-21-21-2100202000000-10-10444-21-21-2100202000000-10-10
χ18444-21-21-2100-20-20000001010444-21-21-2100-20-20000001010444-21-21-2100-20-20000001010
χ1944-41-21-2-1200020-2000000-10144-41-21-2-1200020-2000000-10144-41-21-2-1200020-2000000-101
χ2044-41-21-2-12000-20200000010-144-41-21-2-12000-20200000010-144-41-21-2-12000-20200000010-1
χ2144-4-21-212-10020-2000000-101044-4-21-212-10020-2000000-101044-4-21-212-10020-2000000-1010
χ2244-4-21-212-100-20200000010-1044-4-21-212-100-20200000010-1044-4-21-212-100-20200000010-10
χ238-802-4-24000000000000000008-802-4-24000000000000000008-802-4-2400000000000000000
χ248-80-424-2000000000000000008-80-424-2000000000000000008-80-424-200000000000000000
χ25111111111111111111111111−1+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
χ26111111111111-11-11-1-1-1-11-11-1−1+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−i321−i321−i32−1+i321−i32−1+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−i321+i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32
χ2711111111111-11-111-1-1-1-1-11-11−1+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+i32−1+i321−i321−i321−i321−i321−i32−1+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−i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32
χ2811111111111-1-1-1-111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ2911-11111-1-11111-1-1-111-1-111-1-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ3011-11111-1-1111-1-11-1-1-1111-1-11−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ3111-11111-1-111-111-1-1-1-111-111-1−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ3211-11111-1-111-1-111-111-1-1-1-111−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ33222222222-2-20000-200000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i300001−i300000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i300001+i300000000
χ3422-22222-2-2-2-20000200000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i30000−1+i300000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i30000−1−i300000000
χ352-2022-2-2002-200000002i−2i0000−1+i31−i30−1+i3−1+i31−i31−i300−1+i31−i300000002ζ7−2ζ70000−1−i31+i30−1−i3−1−i31+i31+i300−1−i31+i300000002ζ11−2ζ110000
χ362-2022-2-2002-20000000−2i2i0000−1+i31−i30−1+i3−1+i31−i31−i300−1+i31−i30000000−2ζ72ζ70000−1−i31+i30−1−i3−1−i31+i31+i300−1−i31+i30000000−2ζ112ζ110000
χ372-2022-2-200-22000002-2000000−1+i31−i30−1+i3−1+i31−i31−i3001−i3−1+i300000−1+i31−i3000000−1−i31+i30−1−i3−1−i31+i31+i3001+i3−1−i300000−1−i31+i3000000
χ382-2022-2-200-2200000-22000000−1+i31−i30−1+i3−1+i31−i31−i3001−i3−1+i3000001−i3−1+i3000000−1−i31+i30−1−i3−1−i31+i31+i3001+i3−1−i3000001+i3−1−i3000000
χ394441-21-21-2000202000000-10-1−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i321−i3000−1+i30−1+i30000001−i3201−i32−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i321+i3000−1−i30−1−i30000001+i3201+i32
χ404441-21-21-2000-20-2000000101−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i321−i30001−i301−i3000000−1+i320−1+i32−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i321+i30001+i301+i3000000−1−i320−1−i32
χ41444-21-21-2100202000000-10-10−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i3200−1+i30−1+i30000001−i3201−i320−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i3200−1−i30−1−i30000001+i3201+i320
χ42444-21-21-2100-20-20000001010−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i32001−i301−i3000000−1+i320−1+i320−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i32001+i301+i3000000−1−i320−1−i320
χ4344-41-21-2-1200020-2000000-101−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i32−1+i3000−1+i301−i30000001−i320−1+i32−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i32−1−i3000−1−i301+i30000001+i320−1−i32
χ4444-41-21-2-12000-20200000010-1−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i32−1+i30001−i30−1+i3000000−1+i3201−i32−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i32−1−i30001+i30−1−i3000000−1−i3201+i32
χ4544-4-21-212-10020-2000000-1010−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i31−i3200−1+i301−i30000001−i320−1+i320−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i31+i3200−1−i301+i30000001+i320−1−i320
χ4644-4-21-212-100-20200000010-10−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i31−i32001−i30−1+i3000000−1+i3201−i320−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i31+i32001+i30−1−i3000000−1−i3201+i320
χ478-802-4-2400000000000000000−4+4i34−4i30−1+i32−2i31−i3−2+2i300000000000000000−4−4i34+4i30−1−i32+2i31+i3−2−2i300000000000000000
χ488-80-424-200000000000000000−4+4i34−4i302−2i3−1+i3−2+2i31−i300000000000000000−4−4i34+4i302+2i3−1−i3−2−2i31+i300000000000000000
χ49111111111111111111111111−1−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
χ50111111111111-11-11-1-1-1-11-11-1−1−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+i321+i321+i32−1−i321+i32−1−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+i321−i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32
χ5111111111111-11-111-1-1-1-1-11-11−1−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−i32−1−i321+i321+i321+i321+i321+i32−1−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+i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32
χ5211111111111-1-1-1-111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ5311-11111-1-11111-1-1-111-1-111-1-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ5411-11111-1-1111-1-11-1-1-1111-1-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ5511-11111-1-111-111-1-1-1-111-111-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ5611-11111-1-111-1-111-111-1-1-1-111−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ57222222222-2-20000-200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i300001+i300000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i300001−i300000000
χ5822-22222-2-2-2-20000200000000−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i30000−1−i300000000−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i30000−1+i300000000
χ592-2022-2-2002-200000002i−2i0000−1−i31+i30−1−i3−1−i31+i31+i300−1−i31+i300000002ζ11−2ζ110000−1+i31−i30−1+i3−1+i31−i31−i300−1+i31−i300000002ζ7−2ζ70000
χ602-2022-2-2002-20000000−2i2i0000−1−i31+i30−1−i3−1−i31+i31+i300−1−i31+i30000000−2ζ112ζ110000−1+i31−i30−1+i3−1+i31−i31−i300−1+i31−i30000000−2ζ72ζ70000
χ612-2022-2-200-22000002-2000000−1−i31+i30−1−i3−1−i31+i31+i3001+i3−1−i300000−1−i31+i3000000−1+i31−i30−1+i3−1+i31−i31−i3001−i3−1+i300000−1+i31−i3000000
χ622-2022-2-200-2200000-22000000−1−i31+i30−1−i3−1−i31+i31+i3001+i3−1−i3000001+i3−1−i3000000−1+i31−i30−1+i3−1+i31−i31−i3001−i3−1+i3000001−i3−1+i3000000
χ634441-21-21-2000202000000-10-1−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i321+i3000−1−i30−1−i30000001+i3201+i32−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i321−i3000−1+i30−1+i30000001−i3201−i32
χ644441-21-21-2000-20-2000000101−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i321+i30001+i301+i3000000−1−i320−1−i32−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i321−i30001−i301−i3000000−1+i320−1+i32
χ65444-21-21-2100202000000-10-10−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i3200−1−i30−1−i30000001+i3201+i320−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i3200−1+i30−1+i30000001−i3201−i320
χ66444-21-21-2100-20-20000001010−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i3−1−i32001+i301+i3000000−1−i320−1−i320−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i3−1+i32001−i301−i3000000−1+i320−1+i320
χ6744-41-21-2-1200020-2000000-101−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i32−1−i3000−1−i301+i30000001+i320−1−i32−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i32−1+i3000−1+i301−i30000001−i320−1+i32
χ6844-41-21-2-12000-20200000010-1−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i32−1−i30001+i30−1−i3000000−1−i3201+i32−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i32−1+i30001−i30−1+i3000000−1+i3201−i32
χ6944-4-21-212-10020-2000000-1010−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i31+i3200−1−i301+i30000001+i320−1−i320−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i31−i3200−1+i301−i30000001−i320−1+i320
χ7044-4-21-212-100-20200000010-10−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i31+i32001+i30−1−i3000000−1−i3201+i320−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i31−i32001−i30−1+i3000000−1+i3201−i320
χ718-802-4-2400000000000000000−4−4i34+4i30−1−i32+2i31+i3−2−2i300000000000000000−4+4i34−4i30−1+i32−2i31−i3−2+2i300000000000000000
χ728-80-424-200000000000000000−4−4i34+4i302+2i3−1−i3−2−2i31+i300000000000000000−4+4i34−4i302−2i3−1+i3−2+2i31−i300000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.