Finite Group Databasebeta

← Group #11772892

Character table — Group #11772892

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222222222444444488888888888888888888881616161616161616161616161616161616161616161636363636144144144
order12233336666444666624666666661212121212121212121212124412121212121212121212121212121212121212128888488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1
χ41111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1i−i
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11−ii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1−ii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111−ii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11i−i
χ922222222222-2-2222222-2222222222222-2-2-2-2-2-2-2-200-2-2-2-200000000000000000000000
χ1022222222222-2-222222-22-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200222200000000000000000000000
χ112222-1-1-12-1-1-12222-1-1-12222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000
χ122222-1-1-12-1-1-12222-1-1-12222-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-21111110000000
χ132222-1-1-12-1-1-12222-1-1-1-2-2-2-21111112-1-1-122-1-1-1-1-1-12i−2i-21112i2i−i−i−i−i−i−i−2i−2iiiiiii0000000
χ142222-1-1-12-1-1-12222-1-1-1-2-2-2-21111112-1-1-122-1-1-1-1-1-1−2i2i-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000
χ152222-1-1-12-1-1-1-2-222-1-1-12-222-1-1-1-1-1-12-1-1-1-2-211111100-211100−i3−i3−i3i3i3i300−i3−i3−i3i3i3i30000000
χ162222-1-1-12-1-1-1-2-222-1-1-12-222-1-1-1-1-1-12-1-1-1-2-211111100-211100i3i3i3−i3−i3−i300i3i3i3−i3−i3−i30000000
χ172222-1-1-12-1-1-1-2-222-1-1-1-22-2-21111112-1-1-1-2-2111111002-1-1-100333−3−3−300−3−3−33330000000
χ182222-1-1-12-1-1-1-2-222-1-1-1-22-2-21111112-1-1-1-2-2111111002-1-1-100−3−3−333300333−3−3−30000000
χ19222-12-1-1-12-1-1222-12-1-122-1-122-1-1-1-1-12-1-1-1-122-1-1-1-122-12-1-1-1-12-1-12-1-1-1-12-1-12-1-10000000
χ20222-12-1-1-12-1-1222-12-1-122-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-12-1-111-211-21111-211-2110000000
χ21222-12-1-1-12-1-1222-12-1-1-2-211-2-21111-12-1-1-1-122-1-1-1-12i−2i1-211−i−i2i−i−i2i−i−iii−2iii−2iii0000000
χ22222-12-1-1-12-1-1222-12-1-1-2-211-2-21111-12-1-1-1-122-1-1-1-1−2i2i1-211ii−2iii−2iii−i−i2i−i−i2i−i−i0000000
χ23222-12-1-1-12-1-1-2-22-12-1-12-2-1-122-1-1-1-1-12-1-111-2-21111001-211−i3i30−i3i30−i3i3−i3i30−i3i30−i3i30000000
χ24222-12-1-1-12-1-1-2-22-12-1-12-2-1-122-1-1-1-1-12-1-111-2-21111001-211i3−i30i3−i30i3−i3i3−i30i3−i30i3−i30000000
χ25222-12-1-1-12-1-1-2-22-12-1-1-2211-2-21111-12-1-111-2-2111100-12-1-13−303−303−3−330−330−330000000
χ26222-12-1-1-12-1-1-2-22-12-1-1-2211-2-21111-12-1-111-2-2111100-12-1-1−330−330−333−303−303−30000000
χ27222-1-12-1-1-12-1222-1-12-122-1-1-1-122-1-1-1-12-1-1-1-1-122-1-122-1-12-1-1-1-12-1-1-12-1-1-12-1-1-120000000
χ28222-1-12-1-1-12-1222-1-12-122-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-2-2-1-12-1111-2111-2111-2111-20000000
χ29222-1-12-1-1-12-1222-1-12-1-2-21111-2-211-1-12-1-1-1-1-122-1-12i−2i11-21−i−i−i2i−i−i−i2iiii−2iiii−2i0000000
χ30222-1-12-1-1-12-1222-1-12-1-2-21111-2-211-1-12-1-1-1-1-122-1-1−2i2i11-21iii−2iiii−2i−i−i−i2i−i−i−i2i0000000
χ31222-1-12-1-1-12-1-2-22-1-12-12-2-1-1-1-122-1-1-1-12-11111-2-2110011-21−i3i3i30−i3−i3i30−i3i3i30−i3−i3i300000000
χ32222-1-12-1-1-12-1-2-22-1-12-12-2-1-1-1-122-1-1-1-12-11111-2-2110011-21i3−i3−i30i3i3−i30i3−i3−i30i3i3−i300000000
χ33222-1-12-1-1-12-1-2-22-1-12-1-221111-2-211-1-12-11111-2-21100-1-12-13−3−3033−30−3330−3−3300000000
χ34222-1-12-1-1-12-1-2-22-1-12-1-221111-2-211-1-12-11111-2-21100-1-12-1−3330−3−3303−3−3033−300000000
χ35222-1-1-12-1-1-12222-1-1-1222-1-1-1-1-1-122-1-1-12-1-1-1-1-1-12222-1-1-12-1-1-1-12-12-1-1-1-1-12-12-10000000
χ36222-1-1-12-1-1-12222-1-1-1222-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-2-2-1-1-121111-21-211111-21-210000000
χ37222-1-1-12-1-1-12222-1-1-12-2-2111111-2-2-1-1-12-1-1-1-1-1-1222i−2i111-2−i−i−i−i2i−i2i−iiiii−2ii−2ii0000000
χ38222-1-1-12-1-1-12222-1-1-12-2-2111111-2-2-1-1-12-1-1-1-1-1-122−2i2i111-2iiii−2ii−2ii−i−i−i−i2i−i2i−i0000000
χ39222-1-1-12-1-1-12-2-22-1-1-122-2-1-1-1-1-1-122-1-1-12111111-2-200111-2−i3i3−i3i30i30−i3−i3i3−i3i30i30−i30000000
χ40222-1-1-12-1-1-12-2-22-1-1-122-2-1-1-1-1-1-122-1-1-12111111-2-200111-2i3−i3i3−i30−i30i3i3−i3i3−i30−i30i30000000
χ41222-1-1-12-1-1-12-2-22-1-1-12-22111111-2-2-1-1-12111111-2-200-1-1-123−33−30−303−33−33030−30000000
χ42222-1-1-12-1-1-12-2-22-1-1-12-22111111-2-2-1-1-12111111-2-200-1-1-12−33−33030−33−33−30−3030000000
χ434444444444400-444440000000000-4-4-4-40000000000000000000000000000000000000
χ444444-2-2-24-2-2-200-44-2-2-20000−2i32i3−2i32i3−2i32i3-42220000000000000000000000000000000000000
χ454444-2-2-24-2-2-200-44-2-2-200002i3−2i32i3−2i32i3−2i3-42220000000000000000000000000000000000000
χ46444-24-2-2-24-2-200-4-24-2-200−2i32i300−2i32i32i3−2i32-4220000000000000000000000000000000000000
χ47444-24-2-2-24-2-200-4-24-2-2002i3−2i3002i3−2i3−2i32i32-4220000000000000000000000000000000000000
χ48444-2-24-2-2-24-200-4-2-24-200−2i32i32i3−2i300−2i32i322-420000000000000000000000000000000000000
χ49444-2-24-2-2-24-200-4-2-24-2002i3−2i3−2i32i3002i3−2i322-420000000000000000000000000000000000000
χ50444-2-2-24-2-2-2400-4-2-2-2400−2i32i3−2i32i32i3−2i300222-40000000000000000000000000000000000000
χ51444-2-2-24-2-2-2400-4-2-2-24002i3−2i32i3−2i3−2i32i300222-40000000000000000000000000000000000000
χ5244-444444444000-4-4-4-4000000000000000000000000000000000000000000002i2i−2i−2i000
χ5344-444444444000-4-4-4-400000000000000000000000000000000000000000000−2i−2i2i2i000
χ544-404444-4-4-4-42i−2i00000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000
χ554-404444-4-4-4-42i−2i00000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000
χ564-404444-4-4-4-4−2i2i0000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000
χ574-404444-4-4-4-4−2i2i0000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000
χ5888-88-4-4-48-4-4-4000-8444000000000000000000000000000000000000000000000000000
χ5988-8-48-4-4-48-4-40004-844000000000000000000000000000000000000000000000000000
χ6088-8-4-48-4-4-48-400044-84000000000000000000000000000000000000000000000000000
χ6188-8-4-4-48-4-4-48000444-8000000000000000000000000000000000000000000000000000
χ628-808-4-4-4-84444i−4i00000000000000000004i−4i−2i2i−2i2i−2i2i00000000000000000000000000000
χ638-808-4-4-4-8444−4i4i0000000000000000000−4i4i2i−2i2i−2i2i−2i00000000000000000000000000000
χ648-80-48-4-44-8444i−4i0000000000000000000−2i2i4i−4i−2i2i−2i2i00000000000000000000000000000
χ658-80-48-4-44-844−4i4i00000000000000000002i−2i−4i4i2i−2i2i−2i00000000000000000000000000000
χ668-80-4-48-444-844i−4i0000000000000000000−2i2i−2i2i4i−4i−2i2i00000000000000000000000000000
χ678-80-4-48-444-84−4i4i00000000000000000002i−2i2i−2i−4i4i2i−2i00000000000000000000000000000
χ688-80-4-4-48444-84i−4i0000000000000000000−2i2i−2i2i−2i2i4i−4i00000000000000000000000000000
χ698-80-4-4-48444-8−4i4i00000000000000000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000000

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