Finite Group Databasebeta

← Group #349511

Character table — Group #349511

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111111-1-1-1-1-1-111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-11111111111-1-1-1-1-1-11-1-1-1-11111-1-1111-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-11111111111-1-1-1-1-1-11-1-1-1-11111-1-1111-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-1-1-11111-1-111111-1-1-1-1-1-11-1-111-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-11111-1-111111-1-1-1-1-1-11-1-111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-1-1-11111-1-11-1-1-1-11111-1-11-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-11111-1-11-1-1-1-11111-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-22222222222-200000000-2-2-2-2-200-200000000-2-200000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-222-200000000-2-2-22200-2000000002200000000000000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-20000000022-2-2-2002000000002200000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-20000000022-22200200000000-2-200000000000000000000
χ2122222222-2-2222222-2-22200000000-2-2-22222222222-200-2-2-20000000000-2-2000000000000000000
χ2222222222-2-2222222-2-22200000000-2-2-2-2-2-2-2-2-2-2-222-20022-2000000000022000000000000000000
χ2322222222-2-22222-2-2-2-2-2-200000000-2-2200000000-2-220000222-2-222-2-20000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-200000000-2-2200000000-2-2200002-2-222-2-2220000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2220000000022-22222-2-2-2-2-2-2-200-2-22000000000022000000000000000000
χ2622222222-2-2-2-2-2-222-2-2220000000022-2-2-2-2-22222-2-2-2002220000000000-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222000000002220000-222-2-2-2-2220000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222000000002220000-2-2-22222-2-20000000000000000000000
χ2922-22-22-2-222000022-2-2-2-222-2-2000000222-2-2000000-22-22-202-22-200000000000000000000000000
χ3022-22-22-2-222000022-2-2-2-222-2-20000002-2-222000000-22-2-220-22-2200000000000000000000000000
χ3122-22-22-2-222000022-2-2-2-2-2-222000000222-2-2000000-2-222-20-22-2200000000000000000000000000
χ3222-22-22-2-222000022-2-2-2-2-2-2220000002-2-222000000-2-22-2202-22-200000000000000000000000000
χ3322-22-22-2-2220000-2-2-2-22222-2-2000000-200002i2i−2i−2i002-2200000002i−2i2i−2i002i−2i000000000000000000
χ3422-22-22-2-2220000-2-2-2-22222-2-2000000-20000−2i−2i2i2i002-220000000−2i2i−2i2i00−2i2i000000000000000000
χ3522-22-22-2-2220000-2-2-2-222-2-222000000-200002i2i−2i−2i0022-20000000−2i2i−2i2i002i−2i000000000000000000
χ3622-22-22-2-2220000-2-2-2-222-2-222000000-20000−2i−2i2i2i0022-200000002i−2i2i−2i00−2i2i000000000000000000
χ3722-22-22-2-2-2-200002222-2-200002i2i−2i−2i00-222-2-2000000200-22000002i−2i−2i2i2i−2i00000000000000000000
χ3822-22-22-2-2-2-200002222-2-200002i2i−2i−2i00-2-2-2220000002002-200000−2i2i2i−2i2i−2i00000000000000000000
χ3922-22-22-2-2-2-200002222-2-20000−2i−2i2i2i00-222-2-2000000200-2200000−2i2i2i−2i−2i2i00000000000000000000
χ4022-22-22-2-2-2-200002222-2-20000−2i−2i2i2i00-2-2-2220000002002-2000002i−2i−2i2i−2i2i00000000000000000000
χ4122-22-22-2-2-2-20000-2-2222200002i2i−2i−2i00200002i2i−2i−2i00-2000002-2-220000−2i2i−2i2i000000000000000000
χ4222-22-22-2-2-2-20000-2-2222200002i2i−2i−2i0020000−2i−2i2i2i00-200000-222-20000−2i2i2i−2i000000000000000000
χ4322-22-22-2-2-2-20000-2-222220000−2i−2i2i2i00200002i2i−2i−2i00-200000-222-200002i−2i−2i2i000000000000000000
χ4422-22-22-2-2-2-20000-2-222220000−2i−2i2i2i0020000−2i−2i2i2i00-2000002-2-2200002i−2i2i−2i000000000000000000
χ4522-2-2-2-2222-22i2i−2i−2i002-2002-22-22i−2i2i−2i2i−2i0000000000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ4622-2-2-2-2222-22i2i−2i−2i002-2002-22-22i−2i2i−2i2i−2i00000000000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ4722-2-2-2-2222-22i2i−2i−2i002-200-22-22−2i2i−2i2i2i−2i0000000000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ4822-2-2-2-2222-22i2i−2i−2i002-200-22-22−2i2i−2i2i2i−2i00000000000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ4922-2-2-2-2222-2−2i−2i2i2i002-2002-22-2−2i2i−2i2i−2i2i0000000000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ5022-2-2-2-2222-2−2i−2i2i2i002-2002-22-2−2i2i−2i2i−2i2i00000000000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ5122-2-2-2-2222-2−2i−2i2i2i002-200-22-222i−2i2i−2i−2i2i0000000000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ5222-2-2-2-2222-2−2i−2i2i2i002-200-22-222i−2i2i−2i−2i2i00000000000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ532-2-222-22-2002i−2i2i−2i2-2002-2000000000002i−2i2i−2i2-22-22i−2i000000000000000000i2−i2i2−i22−22−200002−2i2−i200
χ542-2-222-22-2002i−2i2i−2i2-2002-2000000000002i−2i2i−2i2-22-22i−2i000000000000000000−i2i2−i2i2−22−220000−22−i2i200
χ552-2-222-22-2002i−2i2i−2i2-2002-200000000000−2i2i−2i2i-22-222i−2i000000000000000000i2−i2i2−i22−22−20000−22−i2i200
χ562-2-222-22-2002i−2i2i−2i2-2002-200000000000−2i2i−2i2i-22-222i−2i000000000000000000−i2i2−i2i2−22−2200002−2i2−i200
χ572-2-222-22-200−2i2i−2i2i2-2002-2000000000002i−2i2i−2i-22-22−2i2i000000000000000000i2−i2i2−i2−22−2200002−2−i2i200
χ582-2-222-22-200−2i2i−2i2i2-2002-2000000000002i−2i2i−2i-22-22−2i2i000000000000000000−i2i2−i2i22−22−20000−22i2−i200
χ592-2-222-22-200−2i2i−2i2i2-2002-200000000000−2i2i−2i2i2-22-2−2i2i000000000000000000i2−i2i2−i2−22−220000−22i2−i200
χ602-2-222-22-200−2i2i−2i2i2-2002-200000000000−2i2i−2i2i2-22-2−2i2i000000000000000000−i2i2−i2i22−22−200002−2−i2i200
χ61444-44-4-4-44-4000000-44004-4-4400000000000000000000000000000000000000000000000000000
χ62444-44-4-4-44-4000000-4400-444-400000000000000000000000000000000000000000000000000000
χ63444-44-4-4-4-440000004-40000004-4-440000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-440000004-4000000-444-40000000000000000000000000000000000000000000000000
χ6544-4-4-4-444-444i4i−4i−4i00-440000000000−4i4i00000000000000000000000000000000000000000000000
χ6644-4-4-4-444-44−4i−4i4i4i00-4400000000004i−4i00000000000000000000000000000000000000000000000
χ674-444-4-4-440000004-400-44000000000004i−4i−4i4i000000000000000000000000000000000000000000
χ684-444-4-4-440000004-400-4400000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ694-444-4-4-44000000-44004-40000000000000004i−4i−4i4i00000000000000000000000000000000000000
χ704-444-4-4-44000000-44004-4000000000000000−4i4i4i−4i00000000000000000000000000000000000000
χ714-44-4-444-4004-4-440000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ724-44-4-444-4004-4-44000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ734-44-4-444-400-444-40000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ744-44-4-444-400-444-4000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ754-4-444-44-4004i−4i4i−4i-4400-440000000000000000000−4i4i000000000000000000000000000000000000
χ764-4-444-44-400−4i4i−4i4i-4400-4400000000000000000004i−4i000000000000000000000000000000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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