Finite Group Databasebeta

← Group #10594834

Character table — Group #10594834

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444444444444444444446666121212121212121212121212121218181818242424243636
order1222334444666666121212122366666666666121212121212121212121212121244442444446612121212121222221212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111-1-11111111111-11-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-1111-1-1-1-11111-1-1111111-1-1-1-1
χ611111111-1-11111111111-11-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-11111
χ711111111-1-11111111111-11-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1111-111-1-111-1-1-1-111-1-1-1-111-1-111
χ811111111-1-11111111111-11-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1111-1-1-11111-1-1-1-1111111-1-111-1-1
χ9111111-1-111111111-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-111111111-1-11-11-1-1-111-1-11111-1-11-11-11-1
χ10111111-1-111111111-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-111111111-1-1-11-11-1-111-1-111-1-111-11-11-11
χ11111111-1-111111111-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1111-11-111-1-111-1-1-1-1111-11-1-11
χ12111111-1-111111111-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-111-11-1111-1-111-1-111-1-1-11-111-1
χ13111111-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1-111111-1-1-1-111-1-11-1-11-11
χ14111111-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-11111-1-1-1-1-1-111-111-11-1
χ15111111-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-1-1-1-11111-1-1111-1-111-1
χ16111111-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-1-1-1111111-1-1-111-1-11
χ1722222-122222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222220000-1-1-1-1-1-1-1-10000000000
χ1822222-122222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-20000111111110000000000
χ1922222-122-2-22-1-1-122-1-1-1-1-2-1-2-211-1-11111-11122-2-2-1-1-1-1111122-2-2-22000011-1-1-1-1110000000000
χ2022222-122-2-22-1-1-122-1-1-1-1-2-1-2-211-1-11111-11122-2-2-1-1-1-11111-2-2222-20000-1-11111-1-10000000000
χ2122222-1-2-2222-1-1-1221111-2-1-2-211-1-11111-1-1-1-2-2221111-1-1-1-12222-2-2000011-1-111-1-10000000000
χ2222222-1-2-2222-1-1-1221111-2-1-2-211-1-11111-1-1-1-2-2221111-1-1-1-1-2-2-2-2220000-1-111-1-1110000000000
χ2322222-1-2-2-2-22-1-1-12211112-122-1-1-1-1-1-1-1-1-111-2-2-2-21111111122-2-22-20000-1-1-1-111110000000000
χ2422222-1-2-2-2-22-1-1-12211112-122-1-1-1-1-1-1-1-1-111-2-2-2-211111111-2-222-2200001111-1-1-1-10000000000
χ252222-122222-1222-1-122222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000002222000000000000-1-1-1-100
χ262222-122222-1222-1-122222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-2000000000000111100
χ272222-1222-2-2-1222-1-12222-2-111-2-2-1-11111-1-2-2-1-111-1-1-1-1111100000022-2-2000000000000-1-11100
χ282222-1222-2-2-1222-1-12222-2-111-2-2-1-11111-1-2-2-1-111-1-1-1-11111000000-2-22200000000000011-1-100
χ292222-12-2-222-1222-1-1-2-2-2-2-2-111-2-2-1-11111-12211-1-11111-1-1-1-10000002-22-2000000000000-11-1100
χ302222-12-2-222-1222-1-1-2-2-2-2-2-111-2-2-1-11111-12211-1-11111-1-1-1-1000000-22-220000000000001-11-100
χ312222-12-2-2-2-2-1222-1-1-2-2-2-22-1-1-122-1-1-1-1-1-1-1-2-21111111111110000002-2-22000000000000-111-100
χ322222-12-2-2-2-2-1222-1-1-2-2-2-22-1-1-122-1-1-1-1-1-1-1-2-2111111111111000000-222-20000000000001-1-1100
χ332-22-222002i−2i-22-2-22-200000200002-20000-22i−2i002i−2i00002i2i−2i−2i2-22i−2i000000002-2002i−2i0000000000
χ342-22-222002i−2i-22-2-22-200000200002-20000-22i−2i002i−2i00002i2i−2i−2i-22−2i2i00000000-2200−2i2i0000000000
χ352-22-22200−2i2i-22-2-22-200000200002-20000-2−2i2i00−2i2i0000−2i−2i2i2i2-2−2i2i000000002-200−2i2i0000000000
χ362-22-22200−2i2i-22-2-22-200000200002-20000-2−2i2i00−2i2i0000−2i−2i2i2i-222i−2i00000000-22002i−2i0000000000
χ372-22-22-1002i−2i-2-1112-233−3−30-100−i3i3-11−i3−i3i3i31−ii002i−2i33−3−3−i−iii2-22i−2i000000−i3i3-113−3−ii0000000000
χ382-22-22-1002i−2i-2-1112-233−3−30-100−i3i3-11−i3−i3i3i31−ii002i−2i33−3−3−i−iii-22−2i2i000000i3−i31-1−33i−i0000000000
χ392-22-22-1002i−2i-2-1112-2−3−3330-100i3−i3-11i3i3−i3−i31−ii002i−2i−3−333−i−iii2-22i−2i000000i3−i3-11−33−ii0000000000
χ402-22-22-1002i−2i-2-1112-2−3−3330-100i3−i3-11i3i3−i3−i31−ii002i−2i−3−333−i−iii-22−2i2i000000−i3i31-13−3i−i0000000000
χ412-22-22-100−2i2i-2-1112-233−3−30-100i3−i3-11i3i3−i3−i31i−i00−2i2i33−3−3ii−i−i2-2−2i2i000000i3−i3-113−3i−i0000000000
χ422-22-22-100−2i2i-2-1112-233−3−30-100i3−i3-11i3i3−i3−i31i−i00−2i2i33−3−3ii−i−i-222i−2i000000−i3i31-1−33−ii0000000000
χ432-22-22-100−2i2i-2-1112-2−3−3330-100−i3i3-11−i3−i3i3i31i−i00−2i2i−3−333ii−i−i2-2−2i2i000000−i3i3-11−33i−i0000000000
χ442-22-22-100−2i2i-2-1112-2−3−3330-100−i3i3-11−i3−i3i3i31i−i00−2i2i−3−333ii−i−i-222i−2i000000i3−i31-13−3−ii0000000000
χ452-2-22222-200-2-2-22-222-22-2020000-2-200002002-2002-22-200000000000000000000002-22-2000000
χ462-2-22222-200-2-2-22-222-22-2020000-2-200002002-2002-22-20000000000000000000000-22-22000000
χ472-2-2222-2200-2-2-22-22-22-22020000-2-20000200-2200-22-2200000000000000000000002-2-22000000
χ482-2-2222-2200-2-2-22-22-22-22020000-2-20000200-2200-22-220000000000000000000000-222-2000000
χ494444-2-24444-2-2-2-2-2-2-2-2-2-241-2-2-2-21111111-2-2-2-2-2-2111111110000000000000000000000000000
χ504444-2-244-4-4-2-2-2-2-2-2-2-2-2-2-41222211-1-1-1-1122-2-2221111-1-1-1-10000000000000000000000000000
χ514444-2-2-4-444-2-2-2-2-2-22222-41222211-1-1-1-11-2-222-2-2-1-1-1-111110000000000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-2222241-2-2-2-21111111222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ5344-4-44400004-44-4-4-40000040000-440000-4000000000000000000000000000000000000000000
χ5444-4-44-2000042-22-4-423−23−23230-200002-20000200000023−23−232300000000000000000000000000000000
χ5544-4-44-2000042-22-4-4−232323−230-200002-200002000000−232323−2300000000000000000000000000000000
χ5644-4-4-240000-2-44-42200000-2−2i32i3002-2−2i32i3−2i32i32000000000000000000000000000000000000000000
χ5744-4-4-240000-2-44-42200000-22i3−2i3002-22i3−2i32i3−2i32000000000000000000000000000000000000000000
χ5844-4-4-2-20000-22-222223−23−232301−2i32i300-11i3−i3i3−i3-1000000−333−33i−3i3i−3i0000000000000000000000000000
χ5944-4-4-2-20000-22-222223−23−2323012i3−2i300-11−i3i3−i3i3-1000000−333−3−3i3i−3i3i0000000000000000000000000000
χ6044-4-4-2-20000-22-2222−232323−2301−2i32i300-11i3−i3i3−i3-10000003−3−33−3i3i−3i3i0000000000000000000000000000
χ6144-4-4-2-20000-22-2222−232323−23012i3−2i300-11−i3i3−i3i3-10000003−3−333i−3i3i−3i0000000000000000000000000000
χ624-44-4-24004i−4i24-4-4-2200000-20000-22000024i−4i00−2i2i0000−2i−2i2i2i0000000000000000000000000000
χ634-44-4-2400−4i4i24-4-4-2200000-20000-2200002−4i4i002i−2i00002i2i−2i−2i0000000000000000000000000000
χ644-44-4-2-2004i−4i2-222-222323−23−230100−2i32i31-1i3i3−i3−i3-1−2i2i00−2i2i−3−333ii−i−i0000000000000000000000000000
χ654-44-4-2-2004i−4i2-222-22−23−23232301002i3−2i31-1−i3−i3i3i3-1−2i2i00−2i2i33−3−3ii−i−i0000000000000000000000000000
χ664-44-4-2-200−4i4i2-222-222323−23−2301002i3−2i31-1−i3−i3i3i3-12i−2i002i−2i−3−333−i−iii0000000000000000000000000000
χ674-44-4-2-200−4i4i2-222-22−23−2323230100−2i32i31-1i3i3−i3−i3-12i−2i002i−2i33−3−3−i−iii0000000000000000000000000000
χ684-4-444-24-400-422-2-44-22-220-20000220000-2004-400-22-2200000000000000000000000000000000
χ694-4-444-2-4400-422-2-442-22-20-20000220000-200-44002-22-200000000000000000000000000000000
χ704-4-44-244-4002-4-442-24-44-40-20000220000-200-2200-22-2200000000000000000000000000000000
χ714-4-44-24-44002-4-442-2-44-440-20000220000-2002-2002-22-200000000000000000000000000000000
χ724-4-44-2-24-400222-22-2-22-22010000-1-13-3-33100-22001-11-1-333-30000000000000000000000000000
χ734-4-44-2-24-400222-22-2-22-22010000-1-1-333-3100-22001-11-13-3-330000000000000000000000000000
χ744-4-44-2-2-4400222-22-22-22-2010000-1-13-3-331002-200-11-113-3-330000000000000000000000000000
χ754-4-44-2-2-4400222-22-22-22-2010000-1-1-333-31002-200-11-11-333-30000000000000000000000000000

Here i is the imaginary unit (i² = −1).