Finite Group Databasebeta

← Group #398627

Character table — Group #398627

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444444442244444444444444888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1-11-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-11111
χ911111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-11-111-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11111-11-1-11-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-11-1-1111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11-111-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1111111-1-1
χ17222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000002-2002-200000
χ18222222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000-2200-2200000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000002-200-2200000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000-22002-200000
χ2122222222-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000020000-2200-20000
χ2222222222-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000000-200002-20020000
χ2322222222-2-2-2-222-2-222-2-2-2-222-2-2220000000000000000000000000020000-2-20020000
χ2422222222-2-2-2-222-2-222-2-2-2-222-2-22200000000000000000000000000-200002200-20000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-2-22222-2-222-2-200000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-222-2-222-2-22200000000000000000000000000000000
χ2722222222-2-2-2-2-2-222-2-222-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ2822222222-2-2-2-2-2-222-2-222-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ2922-222-2-2-22-22-22-2-2-22-222000000002-22-2000000002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ3022-222-2-2-22-22-22-2-2-22-222000000002-22-200000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ3122-222-2-2-22-22-22-2-2-22-22200000000-22-22000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ3222-222-2-2-22-22-22-2-2-22-22200000000-22-2200000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ3322-222-2-2-2-22-22-22-2-2-2222000000002-2-2200002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ3422-222-2-2-2-22-22-22-2-2-2222000000002-2-220000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ3522-222-2-2-2-22-22-22-2-2-222200000000-222-200002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ3622-222-2-2-2-22-22-22-2-2-222200000000-222-20000−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ372-222-22-2-22-2-222-22-2-222-22i−2i2i−2i2i−2i2i−2i000000002i−2i2i−2i2-22-2000000000000000000000000
χ382-222-22-2-22-2-222-22-2-222-22i−2i2i−2i2i−2i2i−2i00000000−2i2i−2i2i-22-22000000000000000000000000
χ392-222-22-2-22-2-222-22-2-222-2−2i2i−2i2i−2i2i−2i2i000000002i−2i2i−2i-22-22000000000000000000000000
χ402-222-22-2-22-2-222-22-2-222-2−2i2i−2i2i−2i2i−2i2i00000000−2i2i−2i2i2-22-2000000000000000000000000
χ412-222-22-2-22-2-22-22-222-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000002-202i−2i00000000000
χ422-222-22-2-22-2-22-22-222-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000-220−2i2i00000000000
χ432-222-22-2-22-2-22-22-222-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000002-20−2i2i00000000000
χ442-222-22-2-22-2-22-22-222-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000-2202i−2i00000000000
χ452-222-22-2-2-222-22-2-22-22-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000002-22i−2i
χ462-222-22-2-2-222-22-2-22-22-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000-22−2i2i
χ472-222-22-2-2-222-22-2-22-22-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000002-2−2i2i
χ482-222-22-2-2-222-22-2-22-22-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000-222i−2i
χ492-222-22-2-2-222-2-222-22-22-22i−2i−2i2i−2i2i2i−2i00000000000000002-22-22i−2i2i−2i0000000000000000
χ502-222-22-2-2-222-2-222-22-22-22i−2i−2i2i−2i2i2i−2i0000000000000000-22-22−2i2i−2i2i0000000000000000
χ512-222-22-2-2-222-2-222-22-22-2−2i2i2i−2i2i−2i−2i2i00000000000000002-22-2−2i2i−2i2i0000000000000000
χ522-222-22-2-2-222-2-222-22-22-2−2i2i2i−2i2i−2i−2i2i0000000000000000-22-222i−2i2i−2i0000000000000000
χ532-2-22-2-22222-2-222-22-2-22-20000000000002-22-200002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ542-2-22-2-22222-2-222-22-2-22-20000000000002-22-20000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ552-2-22-2-22222-2-222-22-2-22-2000000000000-22-2200002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ562-2-22-2-22222-2-222-22-2-22-2000000000000-22-220000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ572-2-22-2-222-2-222-2-2-22222-20000000000002-2-222-2-2200000000-222-20000000000000000
χ582-2-22-2-222-2-222-2-2-22222-20000000000002-2-22-222-2000000002-2-220000000000000000
χ592-2-22-2-222-2-222-2-2-22222-2000000000000-222-22-2-22000000002-2-220000000000000000
χ602-2-22-2-222-2-222-2-2-22222-2000000000000-222-2-222-200000000-222-20000000000000000
χ6144-444-4-4-44-44-4-4444-44-4-4000000000000000000000000000000000000000000000000
χ6244-444-4-4-4-44-444-4444-4-4-4000000000000000000000000000000000000000000000000
χ634-4-44-4-44444-4-4-4-44-444-44000000000000000000000000000000000000000000000000
χ644-4-44-4-444-4-444444-4-4-4-44000000000000000000000000000000000000000000000000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ6688-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ678-88-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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