Finite Group Databasebeta

← Group #239518

Character table — Group #239518

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222222222444444444422444444444444448888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111
χ911111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ1011111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-11
χ1111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-111-11
χ1211111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-11111-1-11-1
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-11
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-1-1111-1
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-222222-2-222-2-222-2-2-2-222000000000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-222222-2-222-2-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-2-22222-2-2-2-2-222222-2-2-22-2000000000000000000000000000000000000002-22-200
χ2222222222-2-2-22222-2-2-2-2-222222-2-2-22-200000000000000000000000000000000000000-22-2200
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-2-2222-22000000000000000000000000000000002200000000-2-2
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2-2222-2200000000000000000000000000000000-2-20000000022
χ2522222222-2-2-2-2-2-2-22222-22222-22-2-2-22000000000000000000000000000000002-200000000-22
χ2622222222-2-2-2-2-2-2-22222-22222-22-2-2-2200000000000000000000000000000000-22000000002-2
χ2722222222-2-2-2-2-2-2-22222-2-2-2-2-22-2222-2000000000000000000000000000000000000002-2-2200
χ2822222222-2-2-2-2-2-2-22222-2-2-2-2-22-2222-200000000000000000000000000000000000000-222-200
χ2922-2-2-2-22222-222-2-222-2-2-222-2-22-22-2-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ3022-2-2-2-22222-222-2-222-2-2-222-2-22-22-2-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ3122-2-2-2-22222-222-2-222-2-2-2-2-222-22-222-200000000000000000000000000000000002i−2i2i−2i000000
χ3222-2-2-2-22222-222-2-222-2-2-2-2-222-22-222-20000000000000000000000000000000000−2i2i−2i2i000000
χ3322-2-2-2-22222-2-2-222-2-222-222-2-2-222-22-200000000000000000000000000000000002i−2i−2i2i000000
χ3422-2-2-2-22222-2-2-222-2-222-222-2-2-222-22-20000000000000000000000000000000000−2i2i2i−2i000000
χ3522-2-2-2-22222-2-2-222-2-222-2-2-2222-2-22-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ3622-2-2-2-22222-2-2-222-2-222-2-2-2222-2-22-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ3722-2-2-2-222-2-2222-2-2-2-222222-2-222-22-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ3822-2-2-2-222-2-2222-2-2-2-222222-2-222-22-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ3922-2-2-2-222-2-2222-2-2-2-2222-2-222-2-22-222000000000000000022-2-222-2-200000000000000000000
χ4022-2-2-2-222-2-2222-2-2-2-2222-2-222-2-22-2220000000000000000-2-222-2-22200000000000000000000
χ4122-2-2-2-222-2-22-2-22222-2-2222-2-2-2-2-2222000000000000000022-2-2-2-22200000000000000000000
χ4222-2-2-2-222-2-22-2-22222-2-2222-2-2-2-2-22220000000000000000-2-22222-2-200000000000000000000
χ4322-2-2-2-222-2-22-2-22222-2-22-2-222222-2-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ4422-2-2-2-222-2-22-2-22222-2-22-2-222222-2-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ452-222-2-22-22-222-22-22-22-2-20000000000002i−2i002i−2i00000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ462-222-2-22-22-222-22-22-22-2-20000000000002i−2i002i−2i00000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ472-222-2-22-22-222-22-22-22-2-2000000000000−2i2i00−2i2i00000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ482-222-2-22-22-222-22-22-22-2-2000000000000−2i2i00−2i2i00000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ492-222-2-22-22-22-22-22-22-22-20000000000002i−2i00−2i2i00000000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ502-222-2-22-22-22-22-22-22-22-20000000000002i−2i00−2i2i00000000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ512-222-2-22-22-22-22-22-22-22-2000000000000−2i2i002i−2i00000000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ522-222-2-22-22-22-22-22-22-22-2000000000000−2i2i002i−2i00000000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ532-2-2-2222-2-2222-2-22-222-2-200000000002-2002-20000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ542-2-2-2222-2-2222-2-22-222-2-200000000002-2002-20000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ552-2-2-2222-2-2222-2-22-222-2-20000000000-2200-220000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ562-2-2-2222-2-2222-2-22-222-2-20000000000-2200-220000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ572-2-2-2222-2-222-222-22-2-22-200000000002-200-220000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ582-2-2-2222-2-222-222-22-2-22-200000000002-200-220000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ592-2-2-2222-2-222-222-22-2-22-20000000000-22002-20000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ602-2-2-2222-2-222-222-22-2-22-20000000000-22002-20000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ61444-44-4-4-40000000000004i−4i4i−4i000000000000002-22-22i−2i2i−2i0000000000000000000000000000
χ62444-44-4-4-40000000000004i−4i4i−4i00000000000000-22-22−2i2i−2i2i0000000000000000000000000000
χ63444-44-4-4-4000000000000−4i4i−4i4i000000000000002-22-2−2i2i−2i2i0000000000000000000000000000
χ64444-44-4-4-4000000000000−4i4i−4i4i00000000000000-22-222i−2i2i−2i0000000000000000000000000000
χ6544-44-44-4-40000000000004i−4i−4i4i000000000000002i−2i−2i2i-222-20000000000000000000000000000
χ6644-44-44-4-40000000000004i−4i−4i4i00000000000000−2i2i2i−2i2-2-220000000000000000000000000000
χ6744-44-44-4-4000000000000−4i4i4i−4i000000000000002i−2i−2i2i2-2-220000000000000000000000000000
χ6844-44-44-4-4000000000000−4i4i4i−4i00000000000000−2i2i2i−2i-222-20000000000000000000000000000
χ694-444-4-44-4-44-44-44-4-44-444000000000000000000000000000000000000000000000000000000
χ704-444-4-44-4-44-4-44-444-44-44000000000000000000000000000000000000000000000000000000
χ714-4-4-4444-44-4-44-4-444-4-444000000000000000000000000000000000000000000000000000000
χ724-4-4-4444-44-4-4-444-4-444-44000000000000000000000000000000000000000000000000000000
χ738-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000

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