Finite Group Databasebeta

← Group #349531

Character table — Group #349531

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444422444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-11-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111-11
χ121111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-11-1
χ131111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-11
χ141111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1111-1
χ151111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ161111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-22222-2-22-222222222-2-20000220000-200-2-2-20000000000-2-2000000000000000000
χ1822222222222-2-22222-2-22-2-2-2-2-2-2-2-2-2-2-20000220000-200-222000000000022000000000000000000
χ1922222222222-2-2-2-2-2-2-2-22-22222-2-2-2-2220000-2-20000-2002-2-2000000000022000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-2-22222220000-2-20000-2002220000000000-2-2000000000000000000
χ2122222222-2-2-222222222-2-200000000222222-2-22222-2-2-2-20000000000-2-200000000000000000000
χ2222222222-2-2-222222222-2-20000000022-2-2-2-2-2-2-2-2-2-2-222-200000000002200000000000000000000
χ2322222222-2-2-222-2-2-2-222-2-200000000-2-2222222-2-2-2-2-2-2-2200000000002200000000000000000000
χ2422222222-2-2-222-2-2-2-222-2-200000000-2-2-2-2-2-2222222-22220000000000-2-200000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2200000000-2-20000-2-2000020020022-2-222-2-20000000000000000000000
χ2622222222-2-2-2-2-22222-2-2-2200000000-2-20000-2-20000200200-2-222-2-2220000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2200000000220000220000200-20022-2-2-2-2220000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2200000000220000220000200-200-2-22222-2-20000000000000000000000
χ2922-222-2-2-222-2220000-2-2-2222-2-200000022-2-2000000-22-202-22-22-200000000000000000000000000
χ3022-222-2-2-222-2220000-2-2-2222-2-2000000-2-222000000-2-2202-2-22-2200000000000000000000000000
χ3122-222-2-2-222-2220000-2-2-22-2-22200000022-2-2000000-22-20-22-22-2200000000000000000000000000
χ3222-222-2-2-222-2220000-2-2-22-2-222000000-2-222000000-2-220-222-22-200000000000000000000000000
χ3322-222-2-2-222-2-2-2000022-2-222-2-20000000000002i2i−2i−2i2000-2200002i−2i2i−2i2i−2i00000000000000000000
χ3422-222-2-2-222-2-2-2000022-2-222-2-2000000000000−2i−2i2i2i2000-220000−2i2i−2i2i−2i2i00000000000000000000
χ3522-222-2-2-222-2-2-2000022-2-2-2-2220000000000002i2i−2i−2i20002-20000−2i2i−2i2i2i−2i00000000000000000000
χ3622-222-2-2-222-2-2-2000022-2-2-2-222000000000000−2i−2i2i2i20002-200002i−2i2i−2i−2i2i00000000000000000000
χ3722-222-2-2-2-2-22220000-2-22-200002i2i−2i−2i0022-2-20000002-2200000002i−2i−2i2i002i−2i000000000000000000
χ3822-222-2-2-2-2-22220000-2-22-200002i2i−2i−2i00-2-22200000022-20000000−2i2i2i−2i002i−2i000000000000000000
χ3922-222-2-2-2-2-22220000-2-22-20000−2i−2i2i2i0022-2-20000002-220000000−2i2i2i−2i00−2i2i000000000000000000
χ4022-222-2-2-2-2-22220000-2-22-20000−2i−2i2i2i00-2-22200000022-200000002i−2i−2i2i00−2i2i000000000000000000
χ4122-222-2-2-2-2-22-2-20000222200002i2i−2i−2i000000002i2i−2i−2i-2000002-2-220000−2i2i−2i2i000000000000000000
χ4222-222-2-2-2-2-22-2-20000222200002i2i−2i−2i00000000−2i−2i2i2i-200000-222-200002i−2i−2i2i000000000000000000
χ4322-222-2-2-2-2-22-2-2000022220000−2i−2i2i2i000000002i2i−2i−2i-200000-222-20000−2i2i2i−2i000000000000000000
χ4422-222-2-2-2-2-22-2-2000022220000−2i−2i2i2i00000000−2i−2i2i2i-2000002-2-2200002i−2i2i−2i000000000000000000
χ452-222-2-2-220002-22i2i−2i−2i2-200000000002i−2i2i−2i2i−2i002-22-2000000000000000000i2i2−i2−i222−2−200002−2i2−i200
χ462-222-2-2-220002-22i2i−2i−2i2-200000000002i−2i2i−2i2i−2i002-22-2000000000000000000−i2−i2i2i2−2−2220000−22−i2i200
χ472-222-2-2-220002-22i2i−2i−2i2-200000000002i−2i−2i2i−2i2i00-22-22000000000000000000i2i2−i2−i222−2−20000−22−i2i200
χ482-222-2-2-220002-22i2i−2i−2i2-200000000002i−2i−2i2i−2i2i00-22-22000000000000000000−i2−i2i2i2−2−22200002−2i2−i200
χ492-222-2-2-220002-2−2i−2i2i2i2-20000000000−2i2i2i−2i2i−2i00-22-22000000000000000000i2i2−i2−i2−2−22200002−2−i2i200
χ502-222-2-2-220002-2−2i−2i2i2i2-20000000000−2i2i2i−2i2i−2i00-22-22000000000000000000−i2−i2i2i222−2−20000−22i2−i200
χ512-222-2-2-220002-2−2i−2i2i2i2-20000000000−2i2i−2i2i−2i2i002-22-2000000000000000000i2i2−i2−i2−2−2220000−22i2−i200
χ522-222-2-2-220002-2−2i−2i2i2i2-20000000000−2i2i−2i2i−2i2i002-22-2000000000000000000−i2−i2i2i222−2−200002−2−i2i200
χ532-2-2-22-2222-22002-22-200-202i−2i2i−2i2i−2i2i−2i0000002-20000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−2000000
χ542-2-2-22-2222-22002-22-200-202i−2i2i−2i2i−2i2i−2i0000002-20000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22000000
χ552-2-2-22-2222-22002-22-200-20−2i2i−2i2i−2i2i−2i2i0000002-20000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22000000
χ562-2-2-22-2222-22002-22-200-20−2i2i−2i2i−2i2i−2i2i0000002-20000000000000000000000−i2i2−i2i2−i2i2−i2i22−22−2000000
χ572-2-2-22-2222-2200-22-2200-202i−2i2i−2i−2i2i−2i2i000000-220000000000000000000000i2−i2i2−i2−i2i2−i2i22−2−22000000
χ582-2-2-22-2222-2200-22-2200-202i−2i2i−2i−2i2i−2i2i000000-220000000000000000000000−i2i2−i2i2i2−i2i2−i2−222−2000000
χ592-2-2-22-2222-2200-22-2200-20−2i2i−2i2i2i−2i2i−2i000000-220000000000000000000000i2−i2i2−i2−i2i2−i2i2−222−2000000
χ602-2-2-22-2222-2200-22-2200-20−2i2i−2i2i2i−2i2i−2i000000-220000000000000000000000−i2i2−i2i2i2−i2i2−i22−2−22000000
χ6144-4-4-44-44000004i−4i−4i4i0000000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ6244-4-4-44-44000004i−4i−4i4i000000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ6344-4-4-44-4400000−4i4i4i−4i0000000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ6444-4-4-44-4400000−4i4i4i−4i000000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ654-444-4-4-44000-444i4i−4i−4i-440000000000−4i4i0000000000000000000000000000000000000000000000
χ664-444-4-4-44000-44−4i−4i4i4i-4400000000004i−4i0000000000000000000000000000000000000000000000
χ674-44-444-4-44-4-400000000404i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ684-44-444-4-44-4-40000000040−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ694-44-444-4-4-44400000000-4000004-4-44000000000000000000000000000000000000000000000000
χ704-44-444-4-4-44400000000-400000-444-4000000000000000000000000000000000000000000000000
χ714-4-44-444-40004-40000-440000000000004i−4i−4i4i000000000000000000000000000000000000000000
χ724-4-44-444-40004-40000-44000000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ734-4-44-444-4000-4400004-40000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ744-4-44-444-4000-4400004-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ754-4-4-44-444-44-4004-44-4004000000000000000-440000000000000000000000000000000000000000
χ764-4-4-44-444-44-400-44-440040000000000000004-40000000000000000000000000000000000000000
χ77888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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