Finite Group Databasebeta

← Group #116756

Character table — Group #116756

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444442222444444444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91-111-1-11-111-1-1-1-1-1-11111111-1-11-1-111-1-111-1-1iiii−i−i−i−i1111-1-1-1-1i−ii−ii−ii−i11-1-1ii−i−i
χ101-111-1-11-111-1-1-1-1-1-11111111-1-11-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-11111i−i−iii−i−ii-1-111−i−iii
χ111-111-1-11-111-1-1-1-1-1-11111111-1-11-1-111-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−ii−ii−ii−ii11-1-1−i−iii
χ121-111-1-11-111-1-1-1-1-1-11111111-1-11-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-11111−iii−i−iii−i-1-111ii−i−i
χ131-111-1-11-111-1-1-1-1-1-11111111-1-11-1-1-1-111-1-111iiii−i−i−i−i1111-1-1-1-1−iii−i−iii−i-1-111−i−iii
χ141-111-1-11-111-1-1-1-1-1-11111111-1-11-1-1-1-111-1-111iiii−i−i−i−i-1-1-1-11111−ii−ii−ii−ii11-1-1ii−i−i
χ151-111-1-11-111-1-1-1-1-1-11111111-1-11-1-1-1-111-1-111−i−i−i−iiiii1111-1-1-1-1i−i−iii−i−ii-1-111ii−i−i
χ161-111-1-11-111-1-1-1-1-1-11111111-1-11-1-1-1-111-1-111−i−i−i−iiiii-1-1-1-11111i−ii−ii−ii−i11-1-1−i−iii
χ1722222222222222-2-222-2-22-2-22-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ1822222222222222-2-222-2-22-2-22-2-2-2-200000000-2-222-2-222000000000000000000000000
χ19222222222222-2-222-2-222-2-2-2-2-222-20000000000000000000000002200-2-20000000000
χ20222222222222-2-222-2-222-2-2-2-2-222-2000000000000000000000000-2-200220000000000
χ21222222222222-2-2-2-2-2-2-2-2-222-22-2-222222-2-2-2-200000000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-222-22-2-22-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-2-2-222222222-22-2-22-2-2-2000000000000000000000000000000002-22-20000
χ2422222222-2-2-2-222222222-22-2-22-2-2-200000000000000000000000000000000-22-220000
χ2522222222-2-2-2-222-2-222-2-2-2-22-2-22220000000000000000000000000000000000002-22-2
χ2622222222-2-2-2-222-2-222-2-2-2-22-2-2222000000000000000000000000000000000000-22-22
χ2722222222-2-2-2-2-2-222-2-2222-222-2-2-22000000000000000000000000002200-2-200000000
χ2822222222-2-2-2-2-2-222-2-2222-222-2-2-2200000000000000000000000000-2-2002200000000
χ2922222222-2-2-2-2-2-2-2-2-2-2-2-222-22222-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3022222222-2-2-2-2-2-2-2-2-2-2-2-222-22222-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ312-222-2-22-222-2-22222-2-2-2-2-2222-2-22-222-2-2-2-22200000000000000000000000000000000
χ322-222-2-22-222-2-22222-2-2-2-2-2222-2-22-2-2-22222-2-200000000000000000000000000000000
χ332-222-2-22-222-2-222-2-2-2-222-2-2-2222-220000000000000000000000002i−2i00−2i2i0000000000
χ342-222-2-22-222-2-222-2-2-2-222-2-2-2222-22000000000000000000000000−2i2i002i−2i0000000000
χ352-222-2-22-222-2-2-2-22222-2-22-2-2-22-222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362-222-2-22-222-2-2-2-22222-2-22-2-2-22-22200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372-222-2-22-2-2-2222222-2-2-2-222-2-2-22-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ382-222-2-22-2-2-2222222-2-2-2-222-2-2-22-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ392-222-2-22-2-2-22222-2-2-2-2222-22-22-22-2000000000000000000000000002i−2i00−2i2i00000000
χ402-222-2-22-2-2-22222-2-2-2-2222-22-22-22-200000000000000000000000000−2i2i002i−2i00000000
χ412-222-2-22-2-2-222-2-22222-2-2-2-22222-2-20000000000000000000000000000000000002i−2i−2i2i
χ422-222-2-22-2-2-222-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000−2i2i2i−2i
χ432-222-2-22-2-2-222-2-2-2-22222-22-22-2-222000000000000000000000000000000002-2-220000
χ442-222-2-22-2-2-222-2-2-2-22222-22-22-2-22200000000000000000000000000000000-222-20000
χ45444-44-4-4-44-44-4000000000000000000000000000000002-22-22-22-20000000000000000
χ46444-44-4-4-44-44-400000000000000000000000000000000-22-22-22-220000000000000000
χ47444-44-4-4-4-44-44000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ48444-44-4-4-4-44-4400000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4944-44-4-4-4400004i−4i004i−4i00000000002-22-22i−2i2i−2i00000000000000000000000000000000
χ5044-44-4-4-4400004i−4i004i−4i0000000000-22-22−2i2i−2i2i00000000000000000000000000000000
χ5144-44-4-4-440000−4i4i00−4i4i00000000002-22-2−2i2i−2i2i00000000000000000000000000000000
χ5244-44-4-4-440000−4i4i00−4i4i0000000000-22-222i−2i2i−2i00000000000000000000000000000000
χ5344-4-4-444-40000004-4004-400000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5444-4-4-444-40000004-4004-40000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5544-4-4-444-4000000-4400-4400000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ5644-4-4-444-4000000-4400-440000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ574-44-4-44-444-4-44000000000000000000000000000000002-22-2-22-220000000000000000
χ584-44-4-44-444-4-4400000000000000000000000000000000-22-222-22-20000000000000000
χ594-44-4-44-44-444-4000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ604-44-4-44-44-444-400000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ614-4-4444-4-400004i−4i00−4i4i00000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ624-4-4444-4-400004i−4i00−4i4i0000000000-222-22i−2i−2i2i00000000000000000000000000000000
χ634-4-4444-4-40000−4i4i004i−4i00000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ644-4-4444-4-40000−4i4i004i−4i0000000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ654-4-4-44-4440000004-400-4400000000000000002-2-22-222-2000000000000000000000000
χ664-4-4-44-4440000004-400-440000000000000000-222-22-2-22000000000000000000000000
χ674-4-4-44-444000000-44004-400000000000000002-22-2-22-22000000000000000000000000
χ684-4-4-44-444000000-44004-40000000000000000-22-222-22-2000000000000000000000000

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