Finite Group Databasebeta

← Group #67639

Character table — Group #67639

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order1222222234444444466666664412121212121212121212121222446666121212128888888888888888
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
χ5111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111-11-1-1-11ii−i−iii−i−i11-11-1-1-11-111-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ10111-11-1-1-11ii−i−iii−i−i11-11-1-1-11-111-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ11111-11-1-1-11ii−i−iii−i−i11-11-1-1-11-111-1-1iiii−i−i−i−i-11−ii-1-111−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ12111-11-1-1-11ii−i−iii−i−i11-11-1-1-11-111-1-1iiii−i−i−i−i-11−ii-1-111−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ13111-11-1-1-11−i−iii−i−iii11-11-1-1-11-111-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ14111-11-1-1-11−i−iii−i−iii11-11-1-1-11-111-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ15111-11-1-1-11−i−iii−i−iii11-11-1-1-11-111-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ16111-11-1-1-11−i−iii−i−iii11-11-1-1-11-111-1-1−i−i−i−iiiii-11i−i-1-111ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ172222222222-22-22-22-22222222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000
χ18222222222-22-22-22-222222222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000
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
χ2122222222-12-22-22-22-2-1-1-1-1-1-1-1-2-21111-1-111-1-1110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2222222222-12-22-22-22-2-1-1-1-1-1-1-1-2-21111-1-111-1-1110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2322222222-1-22-22-22-22-1-1-1-1-1-1-1-2-2111111-1-111-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2422222222-1-22-22-22-22-1-1-1-1-1-1-1-2-2111111-1-111-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ27222-22-2-2-222i−2i−2i2i2i−2i−2i2i22-22-2-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ28222-22-2-2-22−2i2i2i−2i−2i2i2i−2i22-22-2-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ29222-22-2-2-2-12i2i−2i−2i2i2i−2i−2i-1-11-11112-2-1-111−i−i−i−iiiii2-22i−2i-1-111−i−iii0000000000000000
χ30222-22-2-2-2-12i2i−2i−2i2i2i−2i−2i-1-11-11112-2-1-111−i−i−i−iiiii-22−2i2i11-1-1ii−i−i0000000000000000
χ31222-22-2-2-2-12i−2i−2i2i2i−2i−2i2i-1-11-1111-2211-1-1−i−iiiii−i−i0000−i3i3i3−i33−3−330000000000000000
χ32222-22-2-2-2-12i−2i−2i2i2i−2i−2i2i-1-11-1111-2211-1-1−i−iiiii−i−i0000i3−i3−i3i3−333−30000000000000000
χ33222-22-2-2-2-1−2i2i2i−2i−2i2i2i−2i-1-11-1111-2211-1-1ii−i−i−i−iii0000−i3i3i3−i3−333−30000000000000000
χ34222-22-2-2-2-1−2i2i2i−2i−2i2i2i−2i-1-11-1111-2211-1-1ii−i−i−i−iii0000i3−i3−i3i33−3−330000000000000000
χ35222-22-2-2-2-1−2i−2i2i2i−2i−2i2i2i-1-11-11112-2-1-111iiii−i−i−i−i2-2−2i2i-1-111ii−i−i0000000000000000
χ36222-22-2-2-2-1−2i−2i2i2i−2i−2i2i2i-1-11-11112-2-1-111iiii−i−i−i−i-222i−2i11-1-1−i−iii0000000000000000
χ3722-22-22-2-2202i0−2i0−2i02i2-22-22-2-2000000002i−2i002i−2i0000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ3822-22-22-2-2202i0−2i0−2i02i2-22-22-2-2000000002i−2i002i−2i000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ3922-22-22-2-220−2i02i02i0−2i2-22-22-2-200000000−2i2i00−2i2i0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ4022-22-22-2-220−2i02i02i0−2i2-22-22-2-200000000−2i2i00−2i2i000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ4122-2-2-2-222202020-20-22-2-2-2-222000000002-200-22000000000000−i2i2i2−i2i2−i2−i2i200000000
χ4222-2-2-2-222202020-20-22-2-2-2-222000000002-200-22000000000000i2−i2−i2i2−i2i2i2−i200000000
χ4322-2-2-2-22220-20-202022-2-2-2-22200000000-22002-20000000000002−2−222−2−2200000000
χ4422-2-2-2-22220-20-202022-2-2-2-22200000000-22002-2000000000000−222−2−222−200000000
χ452-222-2-22-222i0−2i0−2i02i0-222-2-22-20000002i−2i002i−2i00000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ462-222-2-22-222i0−2i0−2i02i0-222-2-22-20000002i−2i002i−2i0000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ472-222-2-22-22−2i02i02i0−2i0-222-2-22-2000000−2i2i00−2i2i00000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ482-222-2-22-22−2i02i02i0−2i0-222-2-22-2000000−2i2i00−2i2i0000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ492-22-2-22-2222020-20-20-22-2-22-220000002-200-220000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ502-22-2-22-2222020-20-20-22-2-22-220000002-200-220000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ512-22-2-22-222-20-202020-22-2-22-22000000-22002-200000000000000000000002−2−222−2−22
χ522-22-2-22-222-20-202020-22-2-22-22000000-22002-20000000000000000000000−222−2−222−2
χ5344-44-44-4-4-204i0−4i0−4i04i-22-22-22200000000−2i2i00−2i2i0000000000000000000000000000
χ5444-44-44-4-4-20−4i04i04i0−4i-22-22-222000000002i−2i002i−2i0000000000000000000000000000
χ5544-4-4-4-444-204040-40-4-22222-2-200000000-22002-20000000000000000000000000000
χ5644-4-4-4-444-20-40-40404-22222-2-2000000002-200-220000000000000000000000000000
χ574-444-4-44-4-24i0−4i0−4i04i02-2-222-22000000−2i2i00−2i2i000000000000000000000000000000
χ584-444-4-44-4-2−4i04i04i0−4i02-2-222-220000002i−2i002i−2i000000000000000000000000000000
χ594-44-4-44-44-24040-40-402-222-22-2000000-22002-2000000000000000000000000000000
χ604-44-4-44-44-2-40-4040402-222-22-20000002-200-22000000000000000000000000000000
χ614-4-444-4-44400000000-4-444-4-44000000000000000000000000000000000000000000
χ624-4-444-4-44-20000000022-2-222-200−2i32i3−2i32i3000000000000000000000000000000000000
χ634-4-444-4-44-20000000022-2-222-2002i3−2i32i3−2i3000000000000000000000000000000000000
χ644-4-4-4444-4400000000-4-4-4444-4000000000000000000000000000000000000000000
χ654-4-4-4444-4-200000000222-2-2-2200−2i32i32i3−2i3000000000000000000000000000000000000
χ664-4-4-4444-4-200000000222-2-2-22002i3−2i3−2i32i3000000000000000000000000000000000000

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