Finite Group Databasebeta

← Group #10691539

Character table — Group #10691539

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888121212121616161616161616161616162424242424242424242424242424
order12222234444446664446688881212121212121212881212242424242424242422444488121212122424242424888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1
χ911111111-1-1-1-111111-1-111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−i11-1-11-1i−i11-1-1ii−i−i1-1ii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-111111-1-111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−i11-1-1-11−ii-1-111−i−iii1-1ii−i−i-1-111−i−iii
χ1111111111-1-1-1-111111-1-111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−i-1-1111-1i−i11-1-1ii−i−i-11−i−iii-1-111−i−iii
χ1211111111-1-1-1-111111-1-111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−i-1-111-11−ii-1-111−i−iii-11−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-111111-1-111−i−iii11-1-1-1-1-1-1−ii1-1−i−i−i−iiiii11-1-11-1−ii11-1-1−i−iii1-1−i−iii11-1-1−i−iii
χ1411111111-1-1-1-111111-1-111−i−iii11-1-1-1-1-1-1−ii1-1−i−i−i−iiiii11-1-1-11i−i-1-111ii−i−i1-1−i−iii-1-111ii−i−i
χ1511111111-1-1-1-111111-1-111−i−iii11-1-1-1-1-1-1−ii1-1−i−i−i−iiiii-1-1111-1−ii11-1-1−i−iii-11ii−i−i-1-111ii−i−i
χ1611111111-1-1-1-111111-1-111−i−iii11-1-1-1-1-1-1−ii1-1−i−i−i−iiiii-1-111-11i−i-1-111ii−i−i-11ii−i−i11-1-1−i−iii
χ172222222-22222-2222-2-2-2222222-2-2-2-22222-2-2-2-222-2-222-2-2000000000000000000000000000000
χ182222222-22222-2222-2-2-222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222000000000000000000000000000000
χ192222222-2-2-2-2-2-2222-222222i2i−2i−2i-2-222-2-2-2-2−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ202222222-2-2-2-2-2-2222-22222−2i−2i2i2i-2-222-2-2-2-22i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ21222222-1222222-1-1-1222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-21111111100000000000000
χ23222222-1222222-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111000022-2-2-1-1-1-1111100000000000000
χ24222222-1222222-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2221111-1-1-1-100000000000000
χ25222222-12-2-2-2-22-1-1-12-2-2-1-12i2i−2i−2i-1-11111112i−2i-11−i−i−i−iiiii00002-22i−2i-1-111−i−iii00000000000000
χ26222222-12-2-2-2-22-1-1-12-2-2-1-12i2i−2i−2i-1-11111112i−2i-11−i−i−i−iiiii0000-22−2i2i11-1-1ii−i−i00000000000000
χ27222222-12-2-2-2-22-1-1-12-2-2-1-1−2i−2i2i2i-1-1111111−2i2i-11iiii−i−i−i−i00002-2−2i2i-1-111ii−i−i00000000000000
χ28222222-12-2-2-2-22-1-1-12-2-2-1-1−2i−2i2i2i-1-1111111−2i2i-11iiii−i−i−i−i0000-222i−2i11-1-1−i−iii00000000000000
χ29222222-1-22222-2-1-1-1-2-2-2-1-122221111-1-1-1-1-2-211-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i300000000000000
χ30222222-1-22222-2-1-1-1-2-2-2-1-122221111-1-1-1-1-2-211-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i300000000000000
χ31222222-1-22222-2-1-1-1-2-2-2-1-1-2-2-2-21111-1-1-1-1221111-1-111-1-100000000−i3i3−i3i3i3−i3i3−i300000000000000
χ32222222-1-22222-2-1-1-1-2-2-2-1-1-2-2-2-21111-1-1-1-1221111-1-111-1-100000000i3−i3i3−i3−i3i3−i3i300000000000000
χ33222222-1-2-2-2-2-2-2-1-1-1-222-1-12i2i−2i−2i11-1-11111−2i2i1-1−i−iiiii−i−i00000000−i3i3i3−i33−3−3300000000000000
χ34222222-1-2-2-2-2-2-2-1-1-1-222-1-12i2i−2i−2i11-1-11111−2i2i1-1−i−iiiii−i−i00000000i3−i3−i3i3−333−300000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1-222-1-1−2i−2i2i2i11-1-111112i−2i1-1ii−i−i−i−iii00000000−i3i3i3−i3−333−300000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1-222-1-1−2i−2i2i2i11-1-111112i−2i1-1ii−i−i−i−iii00000000i3−i3−i3i33−3−3300000000000000
χ372222-2-22222-2-22222-2-22-2-2000022-2-222-2-200-220000000022-2-2000000000000-22000000000000
χ382222-2-22222-2-22222-2-22-2-2000022-2-222-2-200-2200000000-2-2220000000000002-2000000000000
χ392222-2-222-2-2222222-22-2-2-200002222-2-22200-2-2000000002222000000000000-2-2000000000000
χ402222-2-222-2-2222222-22-2-2-200002222-2-22200-2-200000000-2-2-2-200000000000022000000000000
χ412222-2-22-222-2-2-222222-2-2-20000-2-22222-2-2002-2000000000000000000000000002i−2i2i−2i00000000
χ422222-2-22-222-2-2-222222-2-2-20000-2-22222-2-2002-200000000000000000000000000−2i2i−2i2i00000000
χ432222-2-22-2-2-222-22222-22-2-20000-2-2-2-2-2-2220022000000000000000000000000002-2-2200000000
χ442222-2-22-2-2-222-22222-22-2-20000-2-2-2-2-2-222002200000000000000000000000000-222-200000000
χ452-22-22-2202i−2i2i−2i0-22-20002-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000000000000000002−2−i2i21+i−1−i1−i−1+i
χ462-22-22-2202i−2i2i−2i0-22-20002-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000−22i2−i2−1−i1+i−1+i1−i
χ472-22-22-2202i−2i2i−2i0-22-20002-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300002i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000000000000000002−2−i2i2−1−i1+i−1+i1−i
χ482-22-22-2202i−2i2i−2i0-22-20002-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300002i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000−22i2−i21+i−1−i1−i−1+i
χ492-22-22-220−2i2i−2i2i0-22-20002-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000000000000000002−2i2−i21−i−1+i1+i−1−i
χ502-22-22-220−2i2i−2i2i0-22-20002-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000−22−i2i2−1+i1−i−1−i1+i
χ512-22-22-220−2i2i−2i2i0-22-20002-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000000000000000002−2i2−i2−1+i1−i−1−i1+i
χ522-22-22-220−2i2i−2i2i0-22-20002-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000−22−i2i21−i−1+i1+i−1−i
χ534444-4-4-2444-4-44-2-2-2-4-44220000-2-222-2-222002-200000000000000000000000000000000000000
χ544444-4-4-24-4-4444-2-2-2-44-4220000-2-2-2-222-2-2002200000000000000000000000000000000000000
χ554444-4-4-2-444-4-4-4-2-2-244-422000022-2-2-2-22200-2200000000000000000000000000000000000000
χ564444-4-4-2-4-4-444-4-2-2-24-44220000222222-2-200-2-200000000000000000000000000000000000000
χ5744-4-400440000-44-4-40000000004-40000000000000000004-40000000000000000000000000000
χ5844-4-400440000-44-4-40000000004-4000000000000000000-440000000000000000000000000000
χ5944-4-4004-4000044-4-4000000000-44000000000000000000004i−4i00000000000000000000000000
χ6044-4-4004-4000044-4-4000000000-4400000000000000000000−4i4i00000000000000000000000000
χ614-44-44-4-204i−4i4i−4i02-22000-224ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ624-44-44-4-204i−4i4i−4i02-22000-22−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ634-44-44-4-20−4i4i−4i4i02-22000-22−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300002i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ644-44-44-4-20−4i4i−4i4i02-22000-224ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300002i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ654-44-4-44404i−4i−4i4i0-44-4000-44000000004i−4i−4i4i000000000000000000000000000000000000000000
χ664-44-4-4440−4i4i4i−4i0-44-4000-4400000000−4i4i4i−4i000000000000000000000000000000000000000000
χ674-44-4-44-204i−4i−4i4i02-220002-200000000−2i2i2i−2i000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000
χ684-44-4-44-204i−4i−4i4i02-220002-200000000−2i2i2i−2i0000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000
χ694-44-4-44-20−4i4i4i−4i02-220002-2000000002i−2i−2i2i0000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000
χ704-44-4-44-20−4i4i4i−4i02-220002-2000000002i−2i−2i2i000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000
χ7188-8-800-480000-8-444000000000-44000000000000000000000000000000000000000000000000
χ7288-8-800-4-800008-4440000000004-4000000000000000000000000000000000000000000000000
χ738-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400000044-40000000000043−430000000000000000000000000000000000000000000000
χ758-8-8800-400000044-400000000000−43430000000000000000000000000000000000000000000000

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