Finite Group Databasebeta

← Group #116270

Character table — Group #116270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444444444444888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
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
χ91-1-1-1-111111-1-11111-1-1-1-111-1-1-11-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−iii−i−i11-1-1
χ101-1-1-1-111111-1-11111-1-1-1-111-1-1-11-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11i−ii−i−i−iii-1-111
χ111-1-1-1-111111-1-11111-1-1-1-111-1-1-11-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11−ii−iiii−i−i-1-111
χ121-1-1-1-111111-1-11111-1-1-1-111-1-1-11-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii−i−iii11-1-1
χ131-1-1-1-111111-1-11111-1-1-1-111-1-1-11-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-11-1−ii−ii−i−iii-1-111
χ141-1-1-1-111111-1-11111-1-1-1-111-1-1-11-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-11−ii−iiii−i−i11-1-1
χ151-1-1-1-111111-1-11111-1-1-1-111-1-1-11-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-11i−ii−i−i−iii11-1-1
χ161-1-1-1-111111-1-11111-1-1-1-111-1-1-11-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-11-1i−ii−iii−i−i-1-111
χ1722222222222222-2-222-2-22-22-2-2-2-2-2000000000000000000000000000022-2-200000000
χ1822222222222222-2-222-2-22-22-2-2-2-2-20000000000000000000000000000-2-22200000000
χ19222222222222-2-222-2-222-2-2-2-2-222-20000000022-2-222-2-2000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-222-200000000-2-222-2-222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-22-222-2-2222-2-222-2-200000000000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-22-222-2-22-2-222-2-22200000000000000000000000000000000
χ2322222222-2-2-2-222222222-22-22-2-2-2-20000000000000000000000000000000000002i−2i2i−2i
χ2422222222-2-2-2-222222222-22-22-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-222-2-222-2-2-2-2-2-2222200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-2-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-222-2-2222-22-22-2-22000000000000000000000000000000002i−2i2i−2i0000
χ2822222222-2-2-2-2-2-222-2-2222-22-22-2-2200000000000000000000000000000000−2i2i−2i2i0000
χ2922222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-200000000000000000000000022-2-2000000000000
χ3022222222-2-2-2-2-2-2-2-2-2-2-2-22222-222-2000000000000000000000000-2-222000000000000
χ312-2-2-2-222222-2-222-2-2-2-2222-2-222-22-200000000000000000000000000002i−2i−2i2i00000000
χ322-2-2-2-222222-2-222-2-2-2-2222-2-222-22-20000000000000000000000000000−2i2i2i−2i00000000
χ332-2-2-2-222222-2-2-2-22222-2-2-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ342-2-2-2-222222-2-2-2-22222-2-2-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ352-2-2-2-222222-2-2-2-2-2-22222-222-2-2-22222-2-2-2-22200000000000000000000000000000000
χ362-2-2-2-222222-2-2-2-2-2-22222-222-2-2-222-2-22222-2-200000000000000000000000000000000
χ372-2-2-2-2222-2-2222222-2-2-2-2-222-22-22-20000000000000000000000000000000000002i−2i−2i2i
χ382-2-2-2-2222-2-2222222-2-2-2-2-222-22-22-2000000000000000000000000000000000000−2i2i2i−2i
χ392-2-2-2-2222-2-22222-2-2-2-222-2-222-22-22000000000000000022-2-2-2-2220000000000000000
χ402-2-2-2-2222-2-22222-2-2-2-222-2-222-22-220000000000000000-2-22222-2-20000000000000000
χ412-2-2-2-2222-2-222-2-22222-2-22-2-22-2-222000000000000000000000000000000002-2-220000
χ422-2-2-2-2222-2-222-2-22222-2-22-2-22-2-22200000000000000000000000000000000-222-20000
χ432-2-2-2-2222-2-222-2-2-2-2222222-2-222-2-20000000000000000000000002-2-22000000000000
χ442-2-2-2-2222-2-222-2-2-2-2222222-2-222-2-2000000000000000000000000-222-2000000000000
χ45444-4-44-4-40000004i−4i004i−4i000000002-22i−2i2-22i−2i00000000000000000000000000000000
χ46444-4-44-4-40000004i−4i004i−4i00000000-22−2i2i-22−2i2i00000000000000000000000000000000
χ47444-4-44-4-4000000−4i4i00−4i4i000000002-2−2i2i2-2−2i2i00000000000000000000000000000000
χ48444-4-44-4-4000000−4i4i00−4i4i00000000-222i−2i-222i−2i00000000000000000000000000000000
χ4944-44-4-44-400004i−4i004i−4i0000000000000000002-22i−2i2-22i−2i000000000000000000000000
χ5044-44-4-44-400004i−4i004i−4i000000000000000000-22−2i2i-22−2i2i000000000000000000000000
χ5144-44-4-44-40000−4i4i00−4i4i0000000000000000002-2−2i2i2-2−2i2i000000000000000000000000
χ5244-44-4-44-40000−4i4i00−4i4i000000000000000000-222i−2i-222i−2i000000000000000000000000
χ5344-4-44-4-444-44-4000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ5444-4-44-4-444-44-400000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ5544-4-44-4-44-44-44000000000000000000000000000000002-2-222-2-220000000000000000
χ5644-4-44-4-44-44-4400000000000000000000000000000000-222-2-222-20000000000000000
χ574-444-4-4-444-4-44000000000000000000000000000000002-22-2-22-220000000000000000
χ584-444-4-4-444-4-4400000000000000000000000000000000-22-222-22-20000000000000000
χ594-444-4-4-44-444-4000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ604-444-4-4-44-444-400000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ614-44-44-44-400004i−4i00−4i4i0000000000000000002i−2i-22−2i2i2-2000000000000000000000000
χ624-44-44-44-400004i−4i00−4i4i000000000000000000−2i2i2-22i−2i-22000000000000000000000000
χ634-44-44-44-40000−4i4i004i−4i0000000000000000002i−2i2-2−2i2i-22000000000000000000000000
χ644-44-44-44-40000−4i4i004i−4i000000000000000000−2i2i-222i−2i2-2000000000000000000000000
χ654-4-4444-4-40000004i−4i00−4i4i000000002-22i−2i-22−2i2i00000000000000000000000000000000
χ664-4-4444-4-40000004i−4i00−4i4i00000000-22−2i2i2-22i−2i00000000000000000000000000000000
χ674-4-4444-4-4000000−4i4i004i−4i000000002-2−2i2i-222i−2i00000000000000000000000000000000
χ684-4-4444-4-4000000−4i4i004i−4i00000000-222i−2i2-2−2i2i00000000000000000000000000000000

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