Finite Group Databasebeta

← Group #411183

Character table — Group #411183

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222222444444444444444444444488888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-111-1-1-1-111-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-1-11111-1-111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ1722222222-2-222-2-22-2-2-2-222222-2-2-2-20000000022-2-2000022-2-200000000000000000000
χ1822222222-2-222-2-22-2-2-2-222222-2-2-2-200000000-2-2220000-2-22200000000000000000000
χ1922222222-2-222-2-22-2-2-2-22-2-2-2-222220000000022-2-20000-2-22200000000000000000000
χ2022222222-2-222-2-22-2-2-2-22-2-2-2-2222200000000-2-222000022-2-200000000000000000000
χ212222-2-2-2-2222222-2-2-2-2-2-20000000022-2-200002i−2i2i−2i000000002i2i−2i−2i0000000000000000
χ222222-2-2-2-2222222-2-2-2-2-2-20000000022-2-20000−2i2i−2i2i00000000−2i−2i2i2i0000000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-200000000-2-22200002i−2i2i−2i00000000−2i−2i2i2i0000000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-200000000-2-2220000−2i2i−2i2i000000002i2i−2i−2i0000000000000000
χ252222-2-2-2-22-2-2-22-222-22-222i2i−2i−2i2i2i−2i−2i000000000000000000000000020-20000002i−2i0000
χ262222-2-2-2-22-2-2-22-222-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000-202000000−2i2i0000
χ272222-2-2-2-22-2-2-22-222-22-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000020-2000000−2i2i0000
χ282222-2-2-2-22-2-2-22-222-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000-2020000002i−2i0000
χ292222-2-2-2-2-22-2-2-222-22-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000020-2000002i−2i000000
χ302222-2-2-2-2-22-2-2-222-22-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000-20200000−2i2i000000
χ312222-2-2-2-2-22-2-2-222-22-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000020-200000−2i2i000000
χ322222-2-2-2-2-22-2-2-222-22-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000-202000002i−2i000000
χ332222-2-2-2-2-2-222-2-2-22222-200000000000022-2-22i−2i−2i2i2i2i−2i−2i000000000000000000000000
χ342222-2-2-2-2-2-222-2-2-22222-200000000000022-2-2−2i2i2i−2i−2i−2i2i2i000000000000000000000000
χ352222-2-2-2-2-2-222-2-2-22222-2000000000000-2-2222i−2i−2i2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-2-2-2-222-2-2-22222-2000000000000-2-222−2i2i2i−2i2i2i−2i−2i000000000000000000000000
χ372-2-2222-2-2222-2-2-22-2-222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000000000000000
χ382-2-2222-2-2222-2-2-22-2-222-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-22-2200000000000000000000000000000000
χ392-2-2222-2-2222-2-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-22-2200000000000000000000000000000000
χ402-2-2222-2-2222-2-2-22-2-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000000000000000
χ412-2-2222-2-2-2-22-222222-2-2-22i−2i2i−2i−2i2i−2i2i0000000000002-22-200002i−2i2i−2i0000000000000000
χ422-2-2222-2-2-2-22-222222-2-2-22i−2i2i−2i−2i2i−2i2i000000000000-22-220000−2i2i−2i2i0000000000000000
χ432-2-2222-2-2-2-22-222222-2-2-2−2i2i−2i2i2i−2i2i−2i0000000000002-22-20000−2i2i−2i2i0000000000000000
χ442-2-2222-2-2-2-22-222222-2-2-2−2i2i−2i2i2i−2i2i−2i000000000000-22-2200002i−2i2i−2i0000000000000000
χ452-2-22-2-222222-2-2-2-222-2-22000000002i−2i−2i2i000000002i−2i−2i2i2-22-200000000000000000000
χ462-2-22-2-222222-2-2-2-222-2-22000000002i−2i−2i2i00000000−2i2i2i−2i-22-2200000000000000000000
χ472-2-22-2-222222-2-2-2-222-2-2200000000−2i2i2i−2i000000002i−2i−2i2i-22-2200000000000000000000
χ482-2-22-2-222222-2-2-2-222-2-2200000000−2i2i2i−2i00000000−2i2i2i−2i2-22-200000000000000000000
χ492-2-22-2-2222-2-22-222-222-2-22-2-222-2-220000000000000000000000000000002i−2i0000002i−2i
χ502-2-22-2-2222-2-22-222-222-2-22-2-222-2-22000000000000000000000000000000−2i2i000000−2i2i
χ512-2-22-2-2222-2-22-222-222-2-2-222-2-222-20000000000000000000000000000002i−2i000000−2i2i
χ522-2-22-2-2222-2-22-222-222-2-2-222-2-222-2000000000000000000000000000000−2i2i0000002i−2i
χ532-2-22-2-222-22-222-222-2-22-22-2-22-222-200000000000000000000000000002i−2i0000002i−2i00
χ542-2-22-2-222-22-222-222-2-22-22-2-22-222-20000000000000000000000000000−2i2i000000−2i2i00
χ552-2-22-2-222-22-222-222-2-22-2-222-22-2-2200000000000000000000000000002i−2i000000−2i2i00
χ562-2-22-2-222-22-222-222-2-22-2-222-22-2-220000000000000000000000000000−2i2i0000002i−2i00
χ572-2-22-2-222-2-22-222-2-2-22220000000000002-2-22000000002-2-22-222-20000000000000000
χ582-2-22-2-222-2-22-222-2-2-22220000000000002-2-2200000000-222-22-2-220000000000000000
χ592-2-22-2-222-2-22-222-2-2-2222000000000000-222-2000000002-2-222-2-220000000000000000
χ602-2-22-2-222-2-22-222-2-2-2222000000000000-222-200000000-222-2-222-20000000000000000
χ61444444444-4-4-44-4-4-44-44-4000000000000000000000000000000000000000000000000
χ6244444444-44-4-4-44-44-44-4-4000000000000000000000000000000000000000000000000
χ634-4-4444-4-44-4-44-44-44-4-444000000000000000000000000000000000000000000000000
χ644-4-4444-4-4-44-444-4-4-444-44000000000000000000000000000000000000000000000000
χ6588-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000
χ6688-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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