Finite Group Databasebeta

← Group #494530

Character table — Group #494530

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444448888888888888888881616161611112222224444444488888888888888888816161616
order124422244488888888224444888816161616161616162488224422244488888888224444888816161616161616162488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ4111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911-1-11-1-111-1ii−i−i1-11-11-11-1i−iii−i−i11-1-1ii−i−i1-1i−i11-1-11-1-111-1ii−i−i1-11-11-11-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ1011-1-11-1-111-1ii−i−i1-11-11-11-1i−iii−i−i-1-111−i−iii-11−ii11-1-11-1-111-1ii−i−i1-11-11-11-1i−iii−i−i-1-111−i−iii-11−ii
χ1111-1-11-1-111-1ii−i−i1-11-1-11-11i−i−i−iii11-1-1ii−i−i-11−ii11-1-11-1-111-1ii−i−i1-11-1-11-11i−i−i−iii11-1-1ii−i−i-11−ii
χ1211-1-11-1-111-1ii−i−i1-11-1-11-11i−i−i−iii-1-111−i−iii1-1i−i11-1-11-1-111-1ii−i−i1-11-1-11-11i−i−i−iii-1-111−i−iii1-1i−i
χ1311-1-11-1-111-1−i−iii1-11-11-11-1−ii−i−iii11-1-1−i−iii1-1−ii11-1-11-1-111-1−i−iii1-11-11-11-1−ii−i−iii11-1-1−i−iii1-1−ii
χ1411-1-11-1-111-1−i−iii1-11-11-11-1−ii−i−iii-1-111ii−i−i-11i−i11-1-11-1-111-1−i−iii1-11-11-11-1−ii−i−iii-1-111ii−i−i-11i−i
χ1511-1-11-1-111-1−i−iii1-11-1-11-11−iiii−i−i11-1-1−i−iii-11i−i11-1-11-1-111-1−i−iii1-11-1-11-11−iiii−i−i11-1-1−i−iii-11i−i
χ1611-1-11-1-111-1−i−iii1-11-1-11-11−iiii−i−i-1-111ii−i−i1-1−ii11-1-11-1-111-1−i−iii1-11-1-11-11−iiii−i−i-1-111ii−i−i1-1−ii
χ1722222222222222-2-2-2-20000-2-2000000000000000022222222222222-2-2-2-20000-2-20000000000000000
χ182222222222-2-2-2-2-2-2-2-200002200000000000000002222222222-2-2-2-2-2-2-2-20000220000000000000000
χ1922222-2-2-2-222-22-2000000000000002−22−22−22−2000022222-2-2-2-222-22-2000000000000002−22−22−22−20000
χ2022222-2-2-2-222-22-200000000000000−22−22−22−22000022222-2-2-2-222-22-200000000000000−22−22−22−220000
χ2122222-2-2-2-22-22-22000000000000002−22−2−22−22000022222-2-2-2-22-22-22000000000000002−22−2−22−220000
χ2222222-2-2-2-22-22-2200000000000000−22−222−22−2000022222-2-2-2-22-22-2200000000000000−22−222−22−20000
χ232222-2-22-22-200002-2-220000002-22-20000000000002222-2-22-22-200002-2-220000002-22-2000000000000
χ242222-2-22-22-200002-2-22000000-22-220000000000002222-2-22-22-200002-2-22000000-22-22000000000000
χ252222-2-22-22-20000-222-22-2-220000000000000000002222-2-22-22-20000-222-22-2-22000000000000000000
χ262222-2-22-22-20000-222-2-222-20000000000000000002222-2-22-22-20000-222-2-222-2000000000000000000
χ2722-2-2222-2-2-22i−2i−2i2i000000000000002−2−22i2−i2−i2i2000022-2-2222-2-2-22i−2i−2i2i000000000000002−2−22i2−i2−i2i20000
χ2822-2-2222-2-2-22i−2i−2i2i00000000000000−222−2−i2i2i2−i2000022-2-2222-2-2-22i−2i−2i2i00000000000000−222−2−i2i2i2−i20000
χ2922-2-2222-2-2-2−2i2i2i−2i000000000000002−2−22−i2i2i2−i2000022-2-2222-2-2-2−2i2i2i−2i000000000000002−2−22−i2i2i2−i20000
χ3022-2-2222-2-2-2−2i2i2i−2i00000000000000−222−2i2−i2−i2i2000022-2-2222-2-2-2−2i2i2i−2i00000000000000−222−2i2−i2−i2i20000
χ3122-2-22-2-222-22i2i−2i−2i-22-220000−2i2i000000000000000022-2-22-2-222-22i2i−2i−2i-22-220000−2i2i0000000000000000
χ3222-2-22-2-222-2−2i−2i2i2i-22-2200002i−2i000000000000000022-2-22-2-222-2−2i−2i2i2i-22-2200002i−2i0000000000000000
χ3322-2-2-22-2-222000022-2-20000002i−2i−2i2i00000000000022-2-2-22-2-222000022-2-20000002i−2i−2i2i000000000000
χ3422-2-2-22-2-222000022-2-2000000−2i2i2i−2i00000000000022-2-2-22-2-222000022-2-2000000−2i2i2i−2i000000000000
χ3522-2-2-22-2-2220000-2-22222-2-200000000000000000022-2-2-22-2-2220000-2-22222-2-2000000000000000000
χ3622-2-2-22-2-2220000-2-222-2-22200000000000000000022-2-2-22-2-2220000-2-222-2-222000000000000000000
χ374444-44-44-4-40000000000000000000000000000004444-44-44-4-4000000000000000000000000000000
χ3844-4-4-4-444-4400000000000000000000000000000044-4-4-4-444-44000000000000000000000000000000
χ398-88i−8i0000000000000000000000000000000000008-88i−8i000000000000000000000000000000000000
χ408-8−8i8i0000000000000000000000000000000000008-8−8i8i000000000000000000000000000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ421111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ43111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ44111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1
χ451111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ461111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ471111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ481111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ4911-1-11-1-111-1ii−i−i1-11-11-11-1i−iii−i−i11-1-1ii−i−i1-1i−i-1-111-111-1-11−i−iii-11-11-11-11−ii−i−iii-1-111−i−iii-11−ii
χ5011-1-11-1-111-1ii−i−i1-11-11-11-1i−iii−i−i-1-111−i−iii-11−ii-1-111-111-1-11−i−iii-11-11-11-11−ii−i−iii11-1-1ii−i−i1-1i−i
χ5111-1-11-1-111-1ii−i−i1-11-1-11-11i−i−i−iii11-1-1ii−i−i-11−ii-1-111-111-1-11−i−iii-11-111-11-1−iiii−i−i-1-111−i−iii1-1i−i
χ5211-1-11-1-111-1ii−i−i1-11-1-11-11i−i−i−iii-1-111−i−iii1-1i−i-1-111-111-1-11−i−iii-11-111-11-1−iiii−i−i11-1-1ii−i−i-11−ii
χ5311-1-11-1-111-1−i−iii1-11-11-11-1−ii−i−iii11-1-1−i−iii1-1−ii-1-111-111-1-11ii−i−i-11-11-11-11i−iii−i−i-1-111ii−i−i-11i−i
χ5411-1-11-1-111-1−i−iii1-11-11-11-1−ii−i−iii-1-111ii−i−i-11i−i-1-111-111-1-11ii−i−i-11-11-11-11i−iii−i−i11-1-1−i−iii1-1−ii
χ5511-1-11-1-111-1−i−iii1-11-1-11-11−iiii−i−i11-1-1−i−iii-11i−i-1-111-111-1-11ii−i−i-11-111-11-1i−i−i−iii-1-111ii−i−i1-1−ii
χ5611-1-11-1-111-1−i−iii1-11-1-11-11−iiii−i−i-1-111ii−i−i1-1−ii-1-111-111-1-11ii−i−i-11-111-11-1i−i−i−iii11-1-1−i−iii-11i−i
χ5722222222222222-2-2-2-20000-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000220000000000000000
χ582222222222-2-2-2-2-2-2-2-20000220000000000000000-2-2-2-2-2-2-2-2-2-2222222220000-2-20000000000000000
χ5922222-2-2-2-222-22-2000000000000002−22−22−22−20000-2-2-2-2-22222-2-22-2200000000000000−22−22−22−220000
χ6022222-2-2-2-222-22-200000000000000−22−22−22−220000-2-2-2-2-22222-2-22-22000000000000002−22−22−22−20000
χ6122222-2-2-2-22-22-22000000000000002−22−2−22−220000-2-2-2-2-22222-22-22-200000000000000−22−222−22−20000
χ6222222-2-2-2-22-22-2200000000000000−22−222−22−20000-2-2-2-2-22222-22-22-2000000000000002−22−2−22−220000
χ632222-2-22-22-200002-2-220000002-22-2000000000000-2-2-2-222-22-220000-222-2000000-22-22000000000000
χ642222-2-22-22-200002-2-22000000-22-22000000000000-2-2-2-222-22-220000-222-20000002-22-2000000000000
χ652222-2-22-22-20000-222-22-2-22000000000000000000-2-2-2-222-22-2200002-2-22-222-2000000000000000000
χ662222-2-22-22-20000-222-2-222-2000000000000000000-2-2-2-222-22-2200002-2-222-2-22000000000000000000
χ6722-2-2222-2-2-22i−2i−2i2i000000000000002−2−22i2−i2−i2i20000-2-222-2-2-2222−2i2i2i−2i00000000000000−222−2−i2i2i2−i20000
χ6822-2-2222-2-2-22i−2i−2i2i00000000000000−222−2−i2i2i2−i20000-2-222-2-2-2222−2i2i2i−2i000000000000002−2−22i2−i2−i2i20000
χ6922-2-2222-2-2-2−2i2i2i−2i000000000000002−2−22−i2i2i2−i20000-2-222-2-2-22222i−2i−2i2i00000000000000−222−2i2−i2−i2i20000
χ7022-2-2222-2-2-2−2i2i2i−2i00000000000000−222−2i2−i2−i2i20000-2-222-2-2-22222i−2i−2i2i000000000000002−2−22−i2i2i2−i20000
χ7122-2-22-2-222-22i2i−2i−2i-22-220000−2i2i0000000000000000-2-222-222-2-22−2i−2i2i2i2-22-200002i−2i0000000000000000
χ7222-2-22-2-222-2−2i−2i2i2i-22-2200002i−2i0000000000000000-2-222-222-2-222i2i−2i−2i2-22-20000−2i2i0000000000000000
χ7322-2-2-22-2-222000022-2-20000002i−2i−2i2i000000000000-2-2222-222-2-20000-2-222000000−2i2i2i−2i000000000000
χ7422-2-2-22-2-222000022-2-2000000−2i2i2i−2i000000000000-2-2222-222-2-20000-2-2220000002i−2i−2i2i000000000000
χ7522-2-2-22-2-2220000-2-22222-2-2000000000000000000-2-2222-222-2-2000022-2-2-2-222000000000000000000
χ7622-2-2-22-2-2220000-2-222-2-222000000000000000000-2-2222-222-2-2000022-2-222-2-2000000000000000000
χ774444-44-44-4-4000000000000000000000000000000-4-4-4-44-44-444000000000000000000000000000000
χ7844-4-4-4-444-44000000000000000000000000000000-4-44444-4-44-4000000000000000000000000000000
χ798-88i−8i000000000000000000000000000000000000-88−8i8i000000000000000000000000000000000000
χ808-8−8i8i000000000000000000000000000000000000-888i−8i000000000000000000000000000000000000

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