Finite Group Databasebeta

← Group #350577

Character table — Group #350577

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444422244444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-111-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-222222222-2-20000220000-2-2-20000-2-20000-2-20000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-20000220000-2-2-20000220000220000000000000000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-2220000-2-20000-2-220000-2-20000220000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-22222220000-2-20000-2-220000220000-2-20000000000000000000000
χ2122222222-2-2222222-2-22200000000222222-2-22222-2-2-2-2-2-2-2000000000000000000000000000000
χ2222222222-2-2222222-2-2220000000022-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-200000000-2-20000-2-2000022200000022-2-20022-2-2000000000000000000
χ2422222222-2-22222-2-2-2-2-2-200000000-2-20000-2-20000222000000-2-22200-2-222000000000000000000
χ2522222222-2-2-2-2-2-222-2-22200000000-2-2222222-2-2-2-2-2-22-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22200000000-2-2-2-2-2-2222222-2-2222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022000022000022-200000022-2-200-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022000022000022-2000000-2-2220022-2-2000000000000000000
χ2922-22-2-2-222-22i2i−2i−2i002-20022-2-22i2i−2i−2i0000002i−2i00000000000000000000000i2i2−i2−i222−2−2i2−i22−2000000
χ3022-22-2-2-222-22i2i−2i−2i002-20022-2-22i2i−2i−2i0000002i−2i00000000000000000000000−i2−i2i2i2−2−222−i2i2−22000000
χ3122-22-2-2-222-22i2i−2i−2i002-200-2-222−2i−2i2i2i0000002i−2i00000000000000000000000i2i2−i2−i222−2−2−i2i2−22000000
χ3222-22-2-2-222-22i2i−2i−2i002-200-2-222−2i−2i2i2i0000002i−2i00000000000000000000000−i2−i2i2i2−2−222i2−i22−2000000
χ3322-22-2-2-222-2−2i−2i2i2i002-20022-2-2−2i−2i2i2i000000−2i2i00000000000000000000000i2i2−i2−i2−2−222i2−i2−22000000
χ3422-22-2-2-222-2−2i−2i2i2i002-20022-2-2−2i−2i2i2i000000−2i2i00000000000000000000000−i2−i2i2i222−2−2−i2i22−2000000
χ3522-22-2-2-222-2−2i−2i2i2i002-200-2-2222i2i−2i−2i000000−2i2i00000000000000000000000i2i2−i2−i2−2−222−i2i22−2000000
χ3622-22-2-2-222-2−2i−2i2i2i002-200-2-2222i2i−2i−2i000000−2i2i00000000000000000000000−i2−i2i2i222−2−2i2−i2−22000000
χ3722-2-2-222-2002i−2i2i−2i2-2002-2000000002i−2i2i2i−2i−2i0022-2-20000000000000000000i2−i2i2−i22−22−200002−2i2−i200
χ3822-2-2-222-2002i−2i2i−2i2-2002-2000000002i−2i2i2i−2i−2i0022-2-20000000000000000000−i2i2−i2i2−22−220000−22−i2i200
χ3922-2-2-222-2002i−2i2i−2i2-2002-2000000002i−2i−2i−2i2i2i00-2-2220000000000000000000i2−i2i2−i22−22−20000−22−i2i200
χ4022-2-2-222-2002i−2i2i−2i2-2002-2000000002i−2i−2i−2i2i2i00-2-2220000000000000000000−i2i2−i2i2−22−2200002−2i2−i200
χ4122-2-2-222-200−2i2i−2i2i2-2002-200000000−2i2i2i2i−2i−2i00-2-2220000000000000000000i2−i2i2−i2−22−2200002−2−i2i200
χ4222-2-2-222-200−2i2i−2i2i2-2002-200000000−2i2i2i2i−2i−2i00-2-2220000000000000000000−i2i2−i2i22−22−20000−22i2−i200
χ4322-2-2-222-200−2i2i−2i2i2-2002-200000000−2i2i−2i−2i2i2i0022-2-20000000000000000000i2−i2i2−i2−22−220000−22i2−i200
χ4422-2-2-222-200−2i2i−2i2i2-2002-200000000−2i2i−2i−2i2i2i0022-2-20000000000000000000−i2i2−i2i22−22−200002−2−i2i200
χ452-2-222-22-22-200002-2-22-2200002i−2i2i−2i002-22-20000002-202-200002i−2i2i−2i2i−2i0000000000000000000000
χ462-2-222-22-22-200002-2-22-2200002i−2i2i−2i00-22-220000002-20-220000−2i2i−2i2i2i−2i0000000000000000000000
χ472-2-222-22-22-200002-2-22-220000−2i2i−2i2i002-22-20000002-202-20000−2i2i−2i2i−2i2i0000000000000000000000
χ482-2-222-22-22-200002-2-22-220000−2i2i−2i2i00-22-220000002-20-2200002i−2i2i−2i−2i2i0000000000000000000000
χ492-2-222-22-22-20000-22-222-200002i−2i2i−2i000000002-22-2-220002-2000000−2i2i2i−2i2i−2i000000000000000000
χ502-2-222-22-22-20000-22-222-200002i−2i2i−2i00000000-22-22-22000-22000000−2i2i−2i2i−2i2i000000000000000000
χ512-2-222-22-22-20000-22-222-20000−2i2i−2i2i000000002-22-2-220002-20000002i−2i−2i2i−2i2i000000000000000000
χ522-2-222-22-22-20000-22-222-20000−2i2i−2i2i00000000-22-22-22000-220000002i−2i2i−2i2i−2i000000000000000000
χ532-2-222-22-2-2200002-22-2-222i−2i2i−2i0000002-22-2000000-220-22002i−2i0000002i−2i−2i2i000000000000000000
χ542-2-222-22-2-2200002-22-2-222i−2i2i−2i000000-22-22000000-2202-2002i−2i000000−2i2i2i−2i000000000000000000
χ552-2-222-22-2-2200002-22-2-22−2i2i−2i2i0000002-22-2000000-220-2200−2i2i000000−2i2i2i−2i000000000000000000
χ562-2-222-22-2-2200002-22-2-22−2i2i−2i2i000000-22-22000000-2202-200−2i2i0000002i−2i−2i2i000000000000000000
χ572-2-222-22-2-220000-222-22-22i−2i2i−2i0000000000002-22-22-2000-22−2i2i2i−2i−2i2i000000000000000000000000
χ582-2-222-22-2-220000-222-22-22i−2i2i−2i000000000000-22-222-20002-2−2i2i−2i2i2i−2i000000000000000000000000
χ592-2-222-22-2-220000-222-22-2−2i2i−2i2i0000000000002-22-22-2000-222i−2i−2i2i2i−2i000000000000000000000000
χ602-2-222-22-2-220000-222-22-2−2i2i−2i2i000000000000-22-222-20002-22i−2i2i−2i−2i2i000000000000000000000000
χ61444-44-4-4-4004-4-440000000000000000000000000000000000000000000002-2-222-2-220000000000
χ62444-44-4-4-4004-4-44000000000000000000000000000000000000000000000-222-2-222-20000000000
χ63444-44-4-4-400-444-40000000000000000000000000000000000000000000002-2-22-222-20000000000
χ64444-44-4-4-400-444-4000000000000000000000000000000000000000000000-222-22-2-220000000000
χ6544-44-4-4-44-444i4i−4i−4i00-440000000000000000−4i4i00000000000000000000000000000000000000000
χ6644-44-4-4-44-44−4i−4i4i4i00-4400000000000000004i−4i00000000000000000000000000000000000000000
χ6744-4-4-444-4004i−4i4i−4i-4400-4400000000−4i4i00000000000000000000000000000000000000000000000
χ6844-4-4-444-400−4i4i−4i4i-4400-44000000004i−4i00000000000000000000000000000000000000000000000
χ694-444-44-4-444000000-4-40000004-4-440000000000000000000000000000000000000000000000000
χ704-444-44-4-444000000-4-4000000-444-40000000000000000000000000000000000000000000000000
χ714-444-44-4-4-4-400000044004i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ724-444-44-4-4-4-40000004400−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ734-44-4-4-4440000004400-4-400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ744-44-4-4-4440000004400-4-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ754-44-4-4-444000000-4-4004400000000000000004-4-440000000000000000000000000000000000000
χ764-44-4-4-444000000-4-400440000000000000000-444-40000000000000000000000000000000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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