Finite Group Databasebeta

← Group #72339057

Character table — Group #72339057

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size1111222244444444444444444888888161616161616161616161616161616161616161616161616323232323232323264646464
order1222224422444444444444444444444222444444444444488888888248888884488
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1111-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-111
χ611111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1
χ711111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-1-11111111111111-1-1-1-111-1-1-1-1-1-111-1-1
χ811111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-111
χ9111111-1-1-1-11-1-1-1iiii−i−i−i−i1-1-111ii−i−i1-1-1-111-111-1-1ii−i−i1ii−i−i11-1-11-1i−iii−i−ii−i1-1
χ10111111-1-1-1-11-1-1-1iiii−i−i−i−i1-1-111ii−i−i1-1-1-111-1-1-111ii−i−i1ii−i−i11-1-1-11i−i−i−iii−ii-11
χ11111111-1-1-1-11-1-1-1iiii−i−i−i−i1-1-111ii−i−i-11-1-11-1111-1-1−i−iii1−i−iii-1-1111-1i−iii−i−i−ii-11
χ12111111-1-1-1-11-1-1-1iiii−i−i−i−i1-1-111ii−i−i-11-1-11-11-1-111−i−iii1−i−iii-1-111-11i−i−i−iiii−i1-1
χ13111111-1-1-1-11-1-1-1−i−i−i−iiiii1-1-111−i−iii1-1-1-111-111-1-1−i−iii1−i−iii11-1-11-1−ii−i−iii−ii1-1
χ14111111-1-1-1-11-1-1-1−i−i−i−iiiii1-1-111−i−iii1-1-1-111-1-1-111−i−iii1−i−iii11-1-1-11−iiii−i−ii−i-11
χ15111111-1-1-1-11-1-1-1−i−i−i−iiiii1-1-111−i−iii-11-1-11-1111-1-1ii−i−i1ii−i−i-1-1111-1−ii−i−iiii−i-11
χ16111111-1-1-1-11-1-1-1−i−i−i−iiiii1-1-111−i−iii-11-1-11-11-1-111ii−i−i1ii−i−i-1-111-11−iiii−i−i−ii1-1
χ17222222222222222222222222222222200-2-2-20000000000-20000000000-2-200000000
χ1822222222222222-2-2-2-2-2-2-2-222222-2-2-2-200-2-2-20000000000-200000000002200000000
χ19222222222222-2-2000000002-2-2-2-20000002-220000002222-2-2-2-2-20000000000000000
χ20222222222222-2-2000000002-2-2-2-20000002-22000000-2-2-2-2-222220000000000000000
χ21222222222222-2-2000000002-2-2-2-2000022-22-2220000000020000-2-2-2-2000000000000
χ22222222222222-2-2000000002-2-2-2-20000-2-2-22-2-2-200000000200002222000000000000
χ23222222-2-2-2-22-22200000000222-2-2000000-2220000002i2i−2i−2i-2−2i−2i2i2i0000000000000000
χ24222222-2-2-2-22-22200000000222-2-2000000-222000000−2i−2i2i2i-22i2i−2i−2i0000000000000000
χ25222222-2-2-2-22-22200000000222-2-200002-22-2-22-20000000020000-2-222000000000000
χ26222222-2-2-2-22-22200000000222-2-20000-222-2-2-22000000002000022-2-2000000000000
χ27222222-2-2-2-22-2-2-22i2i2i2i−2i−2i−2i−2i2-2-2222i2i−2i−2i0022-20000000000-20000000000−2i2i00000000
χ28222222-2-2-2-22-2-2-2−2i−2i−2i−2i2i2i2i2i2-2-222−2i−2i2i2i0022-20000000000-200000000002i−2i00000000
χ2944444444-4-4-440000000000-400000000000000022220000000000000-2-20000000000
χ3044444444-4-4-440000000000-4000000000000000-2-2-2-20000000000000220000000000
χ31444444-4-444-4-40000000000-400000000000000022-2-20000000000000-220000000000
χ32444444-4-444-4-40000000000-4000000000000000-2-22200000000000002-20000000000
χ334444-4-444000-4002222222200000-2-2-2-22-2000-220000000002-22-20000000000000000
χ344444-4-444000-4002222222200000-2-2-2-2-220002-2000000000-22-220000000000000000
χ354444-4-444000-400-2-2-2-2-2-2-2-20000022222-2000-22000000000-22-220000000000000000
χ364444-4-444000-400-2-2-2-2-2-2-2-2000002222-220002-20000000002-22-20000000000000000
χ374444-4-4-4-40004002i2i2i2i−2i−2i−2i−2i00000−2i−2i2i2i22000-2-20000000002i−2i−2i2i0000000000000000
χ384444-4-4-4-40004002i2i2i2i−2i−2i−2i−2i00000−2i−2i2i2i-2-200022000000000−2i2i2i−2i0000000000000000
χ394444-4-4-4-4000400−2i−2i−2i−2i2i2i2i2i000002i2i−2i−2i22000-2-2000000000−2i2i2i−2i0000000000000000
χ404444-4-4-4-4000400−2i−2i−2i−2i2i2i2i2i000002i2i−2i−2i-2-2000220000000002i−2i−2i2i0000000000000000
χ4144-4-4004i−4i00002i−2i2+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i02i−2i2-2000000000002i−2i2-2000000000000000001−i−1+i1+i−1−i0000
χ4244-4-4004i−4i00002i−2i2+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i02i−2i2-200000000000−2i2i-2200000000000000000−1+i1−i−1−i1+i0000
χ4344-4-4004i−4i00002i−2i−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i02i−2i2-2000000000002i−2i2-200000000000000000−1+i1−i−1−i1+i0000
χ4444-4-4004i−4i00002i−2i−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i02i−2i2-200000000000−2i2i-22000000000000000001−i−1+i1+i−1−i0000
χ4544-4-400−4i4i0000−2i2i2−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i0−2i2i2-2000000000002i−2i-2200000000000000000−1−i1+i−1+i1−i0000
χ4644-4-400−4i4i0000−2i2i2−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i0−2i2i2-200000000000−2i2i2-2000000000000000001+i−1−i1−i−1+i0000
χ4744-4-400−4i4i0000−2i2i−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i0−2i2i2-2000000000002i−2i-22000000000000000001+i−1−i1−i−1+i0000
χ4844-4-400−4i4i0000−2i2i−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i0−2i2i2-200000000000−2i2i2-200000000000000000−1−i1+i−1+i1−i0000
χ494-4-444-40000404i−4i2−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i-4−4i4i002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000
χ504-4-444-40000404i−4i−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i-4−4i4i00−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000
χ514-4-444-4000040−4i4i2+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i-44i−4i002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000
χ524-4-444-4000040−4i4i−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i-44i−4i00−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000
χ534-4-44-44004-400002i−2i2i−2i−2i2i−2i2i00000−2i2i2i−2i000000000002i−2i2i−2i000002-22-2000000000000
χ544-4-44-44004-400002i−2i2i−2i−2i2i−2i2i00000−2i2i2i−2i00000000000−2i2i−2i2i00000-22-22000000000000
χ554-4-44-44004-40000−2i2i−2i2i2i−2i2i−2i000002i−2i−2i2i000000000002i−2i2i−2i00000-22-22000000000000
χ564-4-44-44004-40000−2i2i−2i2i2i−2i2i−2i000002i−2i−2i2i00000000000−2i2i−2i2i000002-22-2000000000000
χ574-4-44-4400-4400002-22-22-22-200000-22-22000000000002-2-22000002-2-22000000000000
χ584-4-44-4400-4400002-22-22-22-200000-22-2200000000000-222-200000-222-2000000000000
χ594-4-44-4400-440000-22-22-22-22000002-22-2000000000002-2-2200000-222-2000000000000
χ604-4-44-4400-440000-22-22-22-22000002-22-200000000000-222-2000002-2-22000000000000
χ6188-8-8008i−8i0000−4i4i000000000−4i4i-440000000000000000000000000000000000000000
χ6288-8-800−8i8i00004i−4i0000000004i−4i-440000000000000000000000000000000000000000
χ638-88-800000000444i−4i−4i4i−4i4i4i−4i0-4-4000000000000000000000000000000000000000000
χ648-88-80000000044−4i4i4i−4i4i−4i−4i4i0-4-4000000000000000000000000000000000000000000
χ658-88-800000000-4-44-4-444-4-44044000000000000000000000000000000000000000000
χ668-88-800000000-4-4-444-4-444-4044000000000000000000000000000000000000000000
χ678-8-888-80000-800000000000800000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).