Finite Group Databasebeta

← Group #67642

Character table — Group #67642

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order12222222344444444666666644121212121212121212121212444412121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111-1-1-1-111ii−i−iii−i−i11-1-1-1-111-1iiii−i−i−i−i11-1-1i−i1-1ii−i−i11-1-1ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ10111-1-1-1-111ii−i−iii−i−i11-1-1-1-111-1iiii−i−i−i−i11-1-1i−i1-1ii−i−i11-1-1−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ11111-1-1-1-111ii−i−iii−i−i11-1-1-1-111-1iiii−i−i−i−i11-1-1−ii-11−i−iii-1-111ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ12111-1-1-1-111ii−i−iii−i−i11-1-1-1-111-1iiii−i−i−i−i11-1-1−ii-11−i−iii-1-111−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ13111-1-1-1-111−i−iii−i−iii11-1-1-1-111-1−i−i−i−iiiii11-1-1i−i-11ii−i−i-1-111−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ14111-1-1-1-111−i−iii−i−iii11-1-1-1-111-1−i−i−i−iiiii11-1-1i−i-11ii−i−i-1-111ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ15111-1-1-1-111−i−iii−i−iii11-1-1-1-111-1−i−i−i−iiiii11-1-1−ii1-1−i−iii11-1-1−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ16111-1-1-1-111−i−iii−i−iii11-1-1-1-111-1−i−i−i−iiiii11-1-1−ii1-1−i−iii11-1-1ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ172222222222-22-22-22-22222222-2-222-2-222-2-2-2-2-2-20000000000000000000000000000
χ18222222222-22-22-22-222222222-2-2-2-222-2-222-2-2-2-20000000000000000000000000000
χ1922222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2122222222-12-22-22-22-2-1-1-1-1-1-1-1-2-2-1-111-1-11111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2222222222-12-22-22-22-2-1-1-1-1-1-1-1-2-2-1-111-1-11111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2322222222-1-22-22-22-22-1-1-1-1-1-1-1-2-211-1-111-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2422222222-1-22-22-22-22-1-1-1-1-1-1-1-2-211-1-111-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-1-1-1-122-2-2-1-1-1-111110000000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-1-1-1-1-2-2221111-1-1-1-10000000000000000
χ27222-2-2-2-2222i−2i−2i2i2i−2i−2i2i22-2-2-2-22-222i2i−2i−2i−2i−2i2i2i-2-2220000000000000000000000000000
χ28222-2-2-2-222−2i2i2i−2i−2i2i2i−2i22-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000000000000000
χ29222-2-2-2-22-12i2i−2i−2i2i2i−2i−2i-1-11111-12-2−i−i−i−iiiii-1-1112i−2i2-2−i−iii-1-1110000000000000000
χ30222-2-2-2-22-12i2i−2i−2i2i2i−2i−2i-1-11111-12-2−i−i−i−iiiii-1-111−2i2i-22ii−i−i11-1-10000000000000000
χ31222-2-2-2-22-12i−2i−2i2i2i−2i−2i2i-1-11111-1-22−i−iiiii−i−i11-1-100003−3−33−i3i3i3−i30000000000000000
χ32222-2-2-2-22-12i−2i−2i2i2i−2i−2i2i-1-11111-1-22−i−iiiii−i−i11-1-10000−333−3i3−i3−i3i30000000000000000
χ33222-2-2-2-22-1−2i2i2i−2i−2i2i2i−2i-1-11111-1-22ii−i−i−i−iii11-1-100003−3−33i3−i3−i3i30000000000000000
χ34222-2-2-2-22-1−2i2i2i−2i−2i2i2i−2i-1-11111-1-22ii−i−i−i−iii11-1-10000−333−3−i3i3i3−i30000000000000000
χ35222-2-2-2-22-1−2i−2i2i2i−2i−2i2i2i-1-11111-12-2iiii−i−i−i−i-1-1112i−2i-22−i−iii11-1-10000000000000000
χ36222-2-2-2-22-1−2i−2i2i2i−2i−2i2i2i-1-11111-12-2iiii−i−i−i−i-1-111−2i2i2-2ii−i−i-1-1110000000000000000
χ3722-222-2-2-2202020-20-22-222-2-2-200002-2002-200000000000000002−22−22−22−200000000
χ3822-222-2-2-2202020-20-22-222-2-2-200002-2002-20000000000000000−22−22−22−2200000000
χ3922-222-2-2-220-20-202022-222-2-2-20000-2200-220000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ4022-222-2-2-220-20-202022-222-2-2-20000-2200-220000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ4122-2-2-222-2202i0−2i0−2i02i2-2-2-222-200002i−2i00−2i2i00000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ4222-2-2-222-2202i0−2i0−2i02i2-2-2-222-200002i−2i00−2i2i0000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ4322-2-2-222-220−2i02i02i0−2i2-2-2-222-20000−2i2i002i−2i00000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ4422-2-2-222-220−2i02i02i0−2i2-2-2-222-20000−2i2i002i−2i0000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ452-222-22-2-222020-20-20-222-22-2-2002-2002-2000000000000000000000000002−22−22−22−2
χ462-222-22-2-222020-20-20-222-22-2-2002-2002-200000000000000000000000000−22−22−22−22
χ472-222-22-2-22-20-202020-222-22-2-200-2200-2200000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ482-222-22-2-22-20-202020-222-22-2-200-2200-2200000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ492-22-22-22-222i0−2i0−2i02i0-22-22-22-2002i−2i00−2i2i000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
χ502-22-22-22-222i0−2i0−2i02i0-22-22-22-2002i−2i00−2i2i00000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i
χ512-22-22-22-22−2i02i02i0−2i0-22-22-22-200−2i2i002i−2i000000000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i
χ522-22-22-22-22−2i02i02i0−2i0-22-22-22-200−2i2i002i−2i00000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i
χ5344-444-4-4-4-204040-40-4-22-2-22220000-2200-2200000000000000000000000000000000
χ5444-444-4-4-4-20-40-40404-22-2-222200002-2002-200000000000000000000000000000000
χ5544-4-4-444-4-204i0−4i0−4i04i-2222-2-220000−2i2i002i−2i00000000000000000000000000000000
χ5644-4-4-444-4-20−4i04i04i0−4i-2222-2-2200002i−2i00−2i2i00000000000000000000000000000000
χ574-444-44-4-4-24040-40-402-2-22-22200-2200-220000000000000000000000000000000000
χ584-444-44-4-4-2-40-4040402-2-22-222002-2002-20000000000000000000000000000000000
χ594-44-44-44-4-24i0−4i0−4i04i02-22-22-2200−2i2i002i−2i0000000000000000000000000000000000
χ604-44-44-44-4-2−4i04i04i0−4i02-22-22-22002i−2i00−2i2i0000000000000000000000000000000000
χ614-4-44-4-444400000000-4-44-4-444000000000000000000000000000000000000000000
χ624-4-44-4-444-20000000022-222-2-20000000000−2i32i3−2i32i30000000000000000000000000000
χ634-4-44-4-444-20000000022-222-2-200000000002i3−2i32i3−2i30000000000000000000000000000
χ644-4-4-444-44400000000-4-4-444-44000000000000000000000000000000000000000000
χ654-4-4-444-44-200000000222-2-22-20000000000−2i32i32i3−2i30000000000000000000000000000
χ664-4-4-444-44-200000000222-2-22-200000000002i3−2i3−2i32i30000000000000000000000000000

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