Finite Group Databasebeta

← Group #348741

Character table — Group #348741

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444422224444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1-1-1-111-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-1-1-111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-11111-1-1111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-11111-1-111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-111-1111111-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-111-1111111-1-1-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-222-2-2-20000000022222222-2000000-2-2-2000000-2-2000000000000000000
χ1822222222222222-2-222-2-222-2-2-200000000-2-2-2-2-2-2-2-2-200000022-200000022000000000000000000
χ19222222222222-2-222-2-222-2-222-22222222200000000-20000-2-200-20000-2-200000000000000000000
χ20222222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-2-200000000-200002200-200002200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-220000000000000000222-2-20000222-2-20000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2200000000000000002-2-22200002-2-2220000000000000000000000
χ2322222222-2-2-2-222-2-222-2-2-2-222-2000000002222-2-2-2-2-2000000-2-2200000022000000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-222-200000000-2-2-2-22222-2000000222000000-2-2000000000000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-22222-2-2-2-200000000-20000-2-200200002200000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-2222200000000-20000220020000-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222220000000000000000222-2-20000-2-2-2220000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222200000000000000002-2-2220000-222-2-20000000000000000000000
χ2922-22-2-22-22i2i−2i−2i002-2002-2002i−2i022-2-22i2i−2i−2i00000000000000000000000000i2i2−i2−i222−2−2i2−i22−2000000
χ3022-22-2-22-22i2i−2i−2i002-2002-2002i−2i022-2-22i2i−2i−2i00000000000000000000000000−i2−i2i2i2−2−222−i2i2−22000000
χ3122-22-2-22-22i2i−2i−2i002-2002-2002i−2i0-2-222−2i−2i2i2i00000000000000000000000000i2i2−i2−i222−2−2−i2i2−22000000
χ3222-22-2-22-22i2i−2i−2i002-2002-2002i−2i0-2-222−2i−2i2i2i00000000000000000000000000−i2−i2i2i2−2−222i2−i22−2000000
χ3322-22-2-22-2−2i−2i2i2i002-2002-200−2i2i022-2-2−2i−2i2i2i00000000000000000000000000i2i2−i2−i2−2−222i2−i2−22000000
χ3422-22-2-22-2−2i−2i2i2i002-2002-200−2i2i022-2-2−2i−2i2i2i00000000000000000000000000−i2−i2i2i222−2−2−i2i22−2000000
χ3522-22-2-22-2−2i−2i2i2i002-2002-200−2i2i0-2-2222i2i−2i−2i00000000000000000000000000i2i2−i2−i2−2−222−i2i22−2000000
χ3622-22-2-22-2−2i−2i2i2i002-2002-200−2i2i0-2-2222i2i−2i−2i00000000000000000000000000−i2−i2i2i222−2−2i2−i2−22000000
χ372-222-2-2-222i−2i2i−2i2-2002-2002i−2i0000000000022-2-22i2i−2i−2i0000000000000000002−22−2i2−i2i2−i200002−2i2−i200
χ382-222-2-2-222i−2i2i−2i2-2002-2002i−2i0000000000022-2-22i2i−2i−2i000000000000000000−22−22−i2i2−i2i20000−22−i2i200
χ392-222-2-2-222i−2i2i−2i2-2002-2002i−2i00000000000-2-222−2i−2i2i2i0000000000000000002−22−2i2−i2i2−i20000−22−i2i200
χ402-222-2-2-222i−2i2i−2i2-2002-2002i−2i00000000000-2-222−2i−2i2i2i000000000000000000−22−22−i2i2−i2i200002−2i2−i200
χ412-222-2-2-22−2i2i−2i2i2-2002-200−2i2i0000000000022-2-2−2i−2i2i2i0000000000000000002−22−2−i2i2−i2i200002−2−i2i200
χ422-222-2-2-22−2i2i−2i2i2-2002-200−2i2i0000000000022-2-2−2i−2i2i2i000000000000000000−22−22i2−i2i2−i20000−22i2−i200
χ432-222-2-2-22−2i2i−2i2i2-2002-200−2i2i00000000000-2-2222i2i−2i−2i0000000000000000002−22−2−i2i2−i2i20000−22i2−i200
χ442-222-2-2-22−2i2i−2i2i2-2002-200−2i2i00000000000-2-2222i2i−2i−2i000000000000000000−22−22i2−i2i2−i200002−2−i2i200
χ452-2-2-22-22200002222-2-2-2-20000-22i−2i2i−2i00002i−2i2i−2i000022-22-22i−2i2i−2i000000000000000000000000000
χ462-2-2-22-22200002222-2-2-2-20000-22i−2i2i−2i0000−2i2i−2i2i00002-22-222i−2i−2i2i000000000000000000000000000
χ472-2-2-22-22200002222-2-2-2-20000-2−2i2i−2i2i00002i−2i2i−2i00002-22-22−2i2i2i−2i000000000000000000000000000
χ482-2-2-22-22200002222-2-2-2-20000-2−2i2i−2i2i0000−2i2i−2i2i000022-22-2−2i2i−2i2i000000000000000000000000000
χ492-2-2-22-222000022-2-2-2-2220000200002-22-22i−2i2i−2i0000-2000000−2i2i02i−2i2i−2i2-200000000000000000000
χ502-2-2-22-222000022-2-2-2-2220000200002-22-2−2i2i−2i2i0000-20000002i−2i0−2i2i−2i2i2-200000000000000000000
χ512-2-2-22-222000022-2-2-2-222000020000-22-222i−2i2i−2i0000-2000000−2i2i0−2i2i−2i2i-2200000000000000000000
χ522-2-2-22-222000022-2-2-2-222000020000-22-22−2i2i−2i2i0000-20000002i−2i02i−2i2i−2i-2200000000000000000000
χ532-2-2-22-2220000-2-22222-2-2000022i−2i2i−2i000000002-22-2-20000−2i2i0002i−2i−2i2i002-2000000000000000000
χ542-2-2-22-2220000-2-22222-2-2000022i−2i2i−2i00000000-22-22-20000−2i2i000−2i2i2i−2i00-22000000000000000000
χ552-2-2-22-2220000-2-22222-2-200002−2i2i−2i2i000000002-22-2-200002i−2i000−2i2i2i−2i002-2000000000000000000
χ562-2-2-22-2220000-2-22222-2-200002−2i2i−2i2i00000000-22-22-200002i−2i0002i−2i−2i2i00-22000000000000000000
χ572-2-2-22-2220000-2-2-2-222220000-200002-22-200002-22-222-2-22000000000-22-22000000000000000000
χ582-2-2-22-2220000-2-2-2-222220000-200002-22-20000-22-222-222-2000000000-222-2000000000000000000
χ592-2-2-22-2220000-2-2-2-222220000-20000-22-2200002-22-22-222-20000000002-2-22000000000000000000
χ602-2-2-22-2220000-2-2-2-222220000-20000-22-220000-22-2222-2-220000000002-22-2000000000000000000
χ6144-44-4-44-44i4i−4i−4i00-4400-4400−4i4i00000000000000000000000000000000000000000000000000000
χ6244-44-4-44-4−4i−4i4i4i00-4400-44004i−4i00000000000000000000000000000000000000000000000000000
χ6344-4-4-44-4400004-400-440000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ6444-4-4-44-4400004-400-44000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ6544-4-4-44-440000-44004-400000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ6644-4-4-44-440000-44004-40000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ674-444-4-4-444i−4i4i−4i-4400-4400−4i4i0000000000000000000000000000000000000000000000000000000
χ684-444-4-4-44−4i4i−4i4i-4400-44004i−4i0000000000000000000000000000000000000000000000000000000
χ694-44-4-444-40000004-400-44000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ704-44-4-444-40000004-400-4400000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ714-44-4-444-4000000-44004-40000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ724-44-4-444-4000000-44004-4000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ734-4-4444-4-44-4-44000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ744-4-4444-4-44-4-4400000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ754-4-4444-4-4-444-4000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ764-4-4444-4-4-444-400000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ77888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

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