Finite Group Databasebeta

← Group #10590922

Character table — Group #10590922

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222222222222222244444444444444444444444412121212121212121212121212121212121212121212121236363636
order124423346688881212121224242424242424243666661212121212122424242424242424242424242244666688881212121224242424242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-11-11-1-111-1-111-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111
χ911-1-1-111111ii−i−i-1-1-1-1iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−iiiii−i−i−i−i11-1-11111i−ii−i-1-1-1-1ii−i−iii−i−ii−i1-1
χ1011-1-1-111111ii−i−i-1-1-1-1iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−iiiii−i−i−i−i1-1-1111-1-1i−i−ii-1-111ii−i−i−i−iii−ii-11
χ1111-1-1-111111ii−i−i-1-1-1-1iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−iiiii−i−i−i−i-111-1-1-111−iii−i11-1-1−i−iiiii−i−i−ii-11
χ1211-1-1-111111ii−i−i-1-1-1-1iiii−i−i−i−i1-1-1-1-111111-1-1ii−i−iiiii−i−i−i−i-1-111-1-1-1-1−ii−ii1111−i−iii−i−iiii−i1-1
χ1311-1-1-111111−i−iii-1-1-1-1−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii−i−i−i−iiiii11-1-11111−ii−ii-1-1-1-1−i−iii−i−iii−ii1-1
χ1411-1-1-111111−i−iii-1-1-1-1−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii−i−i−i−iiiii1-1-1111-1-1−iii−i-1-111−i−iiiii−i−ii−i-11
χ1511-1-1-111111−i−iii-1-1-1-1−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii−i−i−i−iiiii-111-1-1-111i−i−ii11-1-1ii−i−i−i−iiii−i-11
χ1611-1-1-111111−i−iii-1-1-1-1−i−i−i−iiiii1-1-1-1-111111-1-1−i−iii−i−i−i−iiiii-1-111-1-1-1-1i−ii−i1111ii−i−iii−i−i−ii1-1
χ17222222-122-1222222-1-122-1-122-1-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1020200-1-1002200-1-10000-1-1-1-10000
χ18222222-122-1222222-1-122-1-122-1-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1-10-20-2001100-2-20011000011110000
χ19222222-122-1-2-2-2-222-1-1-2-211-2-211-12-1-1-1-12-1-1-1-1-1-21-2111111111020200-1-100-2-200-1-1000011110000
χ20222222-122-1-2-2-2-222-1-1-2-211-2-211-12-1-1-1-12-1-1-1-1-1-21-21111111110-20-20011002200110000-1-1-1-10000
χ2122222-122-122222-1-122-1-122-1-122-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-12020-1-1002200-1-100-1-1-1-100000000
χ2222222-122-122222-1-122-1-122-1-122-1-12-1-1-1-12-1-1-1-1-12-12-1-1-1-1-1-1-1-1-20-201100-2-2001100111100000000
χ2322222-122-12-2-2-2-2-1-12211-2-211-2-2-1-12-1-1-1-12-1-1-1-11-21-2111111112020-1-100-2-200-1-100111100000000
χ2422222-122-12-2-2-2-2-1-12211-2-211-2-2-1-12-1-1-1-12-1-1-1-11-21-211111111-20-20110022001100-1-1-1-100000000
χ252222-222-2222-22-2222222-2-222-2-22-2-2-2-22-2-2-2-222-22-2222-2-222-2-20000000000000000000000000000
χ262222-222-222-22-222222-2-222-2-2222-2-2-2-22-2-2-2-2222-22-2-2-222-2-2220000000000000000000000000000
χ272222-22-1-22-12-22-222-1-122112211-1-2111-1-2111-1-1-2-1-2-1-1-111-1-111000000−i3i3000000−i3i30000−i3i3−i3i30000
χ282222-22-1-22-12-22-222-1-122112211-1-2111-1-2111-1-1-2-1-2-1-1-111-1-111000000i3−i3000000i3−i30000i3−i3i3−i30000
χ292222-22-1-22-1-22-2222-1-1-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1212111-1-111-1-1000000−i3i3000000−i3i30000i3−i3i3−i30000
χ302222-22-1-22-1-22-2222-1-1-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1212111-1-111-1-1000000i3−i3000000i3−i30000−i3i3−i3i30000
χ312222-2-12-2-122-22-2-1-122-1-1-2-2-1-1-2-2-11-211-11-211-1-11212-1-111-1-1110000−i3i3000000−i3i300−i3i3−i3i300000000
χ322222-2-12-2-122-22-2-1-122-1-1-2-2-1-1-2-2-11-211-11-211-1-11212-1-111-1-1110000i3−i3000000i3−i300i3−i3i3−i300000000
χ332222-2-12-2-12-22-22-1-12211221122-11-211-11-211-1-1-1-2-1-211-1-111-1-10000−i3i3000000−i3i300i3−i3i3−i300000000
χ342222-2-12-2-12-22-22-1-12211221122-11-211-11-211-1-1-1-2-1-211-1-111-1-10000i3−i3000000i3−i300−i3i3−i3i300000000
χ3522-2-2222-2222i−2i−2i2i-2-2-2-22i2i−2i−2i−2i−2i2i2i222222-2-2-2-2-2-2−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ3622-2-2222-222−2i2i2i−2i-2-2-2-2−2i−2i2i2i2i2i−2i−2i222222-2-2-2-2-2-22i−2i−2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ3722-2-222-1-22-12i−2i−2i2i-2-2112i2iii−2i−2i−i−i-12-1-1-1-1-211111−2i−i2ii−i−iiiii−i−i000000−i3i3000000i3−i300003−3−330000
χ3822-2-222-1-22-12i−2i−2i2i-2-2112i2iii−2i−2i−i−i-12-1-1-1-1-211111−2i−i2ii−i−iiiii−i−i000000i3−i3000000−i3i30000−333−30000
χ3922-2-222-1-22-1−2i2i2i−2i-2-211−2i−2i−i−i2i2iii-12-1-1-1-1-2111112ii−2i−iii−i−i−i−iii000000−i3i3000000i3−i30000−333−30000
χ4022-2-222-1-22-1−2i2i2i−2i-2-211−2i−2i−i−i2i2iii-12-1-1-1-1-2111112ii−2i−iii−i−i−i−iii000000i3−i3000000−i3i300003−3−330000
χ4122-2-22-12-2-122i−2i−2i2i11-2-2−i−i−2i−2iii2i2i-1-12-1-1-11-21111i2i−i−2i−i−iiiii−i−i0000−i3i3000000i3−i3003−3−3300000000
χ4222-2-22-12-2-122i−2i−2i2i11-2-2−i−i−2i−2iii2i2i-1-12-1-1-11-21111i2i−i−2i−i−iiiii−i−i0000i3−i3000000−i3i300−333−300000000
χ4322-2-22-12-2-12−2i2i2i−2i11-2-2ii2i2i−i−i−2i−2i-1-12-1-1-11-21111−i−2ii2iii−i−i−i−iii0000−i3i3000000i3−i300−333−300000000
χ4422-2-22-12-2-12−2i2i2i−2i11-2-2ii2i2i−i−i−2i−2i-1-12-1-1-11-21111−i−2ii2iii−i−i−i−iii0000i3−i3000000−i3i3003−3−3300000000
χ4522-2-2-22-122-12i2i−2i−2i-2-2112i2i−i−i−2i−2iii-1-2111-12-1-1-1112i−i−2ii−i−i−i−iiiii020-200-1-1002i−2i00110000−i−iii0000
χ4622-2-2-22-122-12i2i−2i−2i-2-2112i2i−i−i−2i−2iii-1-2111-12-1-1-1112i−i−2ii−i−i−i−iiiii0-202001100−2i2i00-1-10000ii−i−i0000
χ4722-2-2-22-122-1−2i−2i2i2i-2-211−2i−2iii2i2i−i−i-1-2111-12-1-1-111−2ii2i−iiiii−i−i−i−i020-200-1-100−2i2i00110000ii−i−i0000
χ4822-2-2-22-122-1−2i−2i2i2i-2-211−2i−2iii2i2i−i−i-1-2111-12-1-1-111−2ii2i−iiiii−i−i−i−i0-2020011002i−2i00-1-10000−i−iii0000
χ4922-2-2-2-122-122i2i−2i−2i11-2-2−i−i2i2iii−2i−2i-11-211-1-12-1-111−i2ii−2i−i−i−i−iiiii20-20-1-1002i−2i001100−i−iii00000000
χ5022-2-2-2-122-122i2i−2i−2i11-2-2−i−i2i2iii−2i−2i-11-211-1-12-1-111−i2ii−2i−i−i−i−iiiii-20201100−2i2i00-1-100ii−i−i00000000
χ5122-2-2-2-122-12−2i−2i2i2i11-2-2ii−2i−2i−i−i2i2i-11-211-1-12-1-111i−2i−i2iiiii−i−i−i−i20-20-1-100−2i2i001100ii−i−i00000000
χ5222-2-2-2-122-12−2i−2i2i2i11-2-2ii−2i−2i−i−i2i2i-11-211-1-12-1-111i−2i−i2iiiii−i−i−i−i-202011002i−2i00-1-100−i−iii00000000
χ5344444-2-24-2-24444-2-2-2-2-2-2-2-2-2-2-2-21-2-2111-2-21111-2-2-2-2111111110000000000000000000000000000
χ5444444-2-24-2-2-4-4-4-4-2-2-2-2222222221-2-2111-2-211112222-1-1-1-1-1-1-1-10000000000000000000000000000
χ554444-4-2-2-4-2-24-44-4-2-2-2-2-2-222-2-222122-1-1122-1-1112-22-211-1-111-1-10000000000000000000000000000
χ564444-4-2-2-4-2-2-44-44-2-2-2-222-2-222-2-2122-1-1122-1-111-22-22-1-111-1-1110000000000000000000000000000
χ5744-4-44-2-2-4-2-24i−4i−4i4i2222−2i−2i2i2i2i2i−2i−2i1-2-211122-1-1-1-12i−2i−2i2iii−i−i−i−iii0000000000000000000000000000
χ5844-4-44-2-2-4-2-2−4i4i4i−4i22222i2i−2i−2i−2i−2i2i2i1-2-211122-1-1-1-1−2i2i2i−2i−i−iiiii−i−i0000000000000000000000000000
χ5944-4-4-4-2-24-2-24i4i−4i−4i2222−2i−2i−2i−2i2i2i2i2i122-1-11-2-211-1-1−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000
χ6044-4-4-4-2-24-2-2−4i−4i4i4i22222i2i2i2i−2i−2i−2i−2i122-1-11-2-211-1-12i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000
χ614-44i−4i0440-4-400004i−4i4i−4i0000000040000-400004i−4i0000000000000000000000000000000000000000
χ624-44i−4i04-20-4200004i−4i−2i2i002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ23-2000020000−2i2i0000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000
χ634-44i−4i04-20-4200004i−4i−2i2i00−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23-2000020000−2i2i000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000
χ644-44i−4i0-2402-40000−2i2i4i−4i−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ1300-2000020000−2i2i0000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000
χ654-44i−4i0-2402-40000−2i2i4i−4i2ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ1300-2000020000−2i2i00002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000
χ664-44i−4i0-2-20220000−2i2i−2i2i−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ132ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ231003-3-1003i−3ii−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000
χ674-44i−4i0-2-20220000−2i2i−2i2i−2ζ7+2ζ232ζ7−2ζ23−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ132ζ7−2ζ23−2ζ7+2ζ23100-33-100−3i3ii−i0000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000
χ684-44i−4i0-2-20220000−2i2i−2i2i2ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ13−2ζ7+2ζ232ζ7−2ζ23100-33-100−3i3ii−i0000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000
χ694-44i−4i0-2-20220000−2i2i−2i2i2ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ231003-3-1003i−3ii−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000
χ704-4−4i4i0440-4-40000−4i4i−4i4i0000000040000-40000−4i4i0000000000000000000000000000000000000000
χ714-4−4i4i04-20-420000−4i4i2i−2i00−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13-20000200002i−2i000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000
χ724-4−4i4i04-20-420000−4i4i2i−2i002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13-20000200002i−2i0000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000
χ734-4−4i4i0-2402-400002i−2i−4i4i2ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ2300-20000200002i−2i00002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000
χ744-4−4i4i0-2402-400002i−2i−4i4i−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ2300-20000200002i−2i0000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000
χ754-4−4i4i0-2-202200002i−2i2i−2i2ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ131003-3-100−3i3i−ii0000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000
χ764-4−4i4i0-2-202200002i−2i2i−2i2ζ5−2ζ13−2ζ5+2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ5+2ζ132ζ5−2ζ13100-33-1003i−3i−ii0000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000
χ774-4−4i4i0-2-202200002i−2i2i−2i−2ζ5+2ζ132ζ5−2ζ13−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ13100-33-1003i−3i−ii0000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000
χ784-4−4i4i0-2-202200002i−2i2i−2i−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ232ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ131003-3-100−3i3i−ii0000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000

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