Finite Group Databasebeta

← Group #349525

Character table — Group #349525

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
χ3111111111111111111111111111111-1-1-1-1111-1-1-1-1111-1-11-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1111-1-1-1-1111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111-1-1-1-1111-1-11111-1-1-1-111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111-1-1-1-1111-1-11111-1-1-1-111111-1-1-1-1-1-111111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111-11
χ121111111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-11-1
χ131111111111111-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ161111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-22222-2-22-2-2222222220000-2220000-2-2-200-200000000-2-200000000000000000000
χ1822222222222-2-22222-2-22-2-2-2-2-2-2-2-2-2-20000-2220000-22200-2000000002200000000000000000000
χ1922222222222-2-2-2-2-2-2-2-22222222-2-2-2-20000-2-2-20000-2-2-2002000000002200000000000000000000
χ2022222222222-2-2-2-2-2-2-2-2222-2-2-2-222220000-2-2-20000-22200200000000-2-200000000000000000000
χ2122222222-2-2-222222222-222000000002222-2-2-22222-200-2-2-20000000000-2-2000000000000000000
χ2222222222-2-2-222222222-22200000000-2-2-2-2-2-2-2-2-2-2-2-20022-2000000000022000000000000000000
χ2322222222-2-2-222-2-2-2-222-2-2-2000000002222-222-2-2-2-2-200-2-22000000000022000000000000000000
χ2422222222-2-2-222-2-2-2-222-2-2-200000000-2-2-2-2-2222222-2002220000000000-2-2000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-20000000000002-2-2000020000222-2-222-2-20000000000000000000000
χ2622222222-2-2-2-2-22222-2-2-2-2-20000000000002-2-20000200002-2-222-2-2220000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000222000020000-222-2-2-2-2220000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222000000000000222000020000-2-2-22222-2-20000000000000000000000
χ29222-22-2-2-222-2220000-2-2-20022-2-2000022-2-22000000-22-22-202-22-200000000000000000000000000
χ30222-22-2-2-222-2220000-2-2-20022-2-20000-2-2222000000-22-2-220-22-2200000000000000000000000000
χ31222-22-2-2-222-2220000-2-2-200-2-222000022-2-22000000-2-222-20-22-2200000000000000000000000000
χ32222-22-2-2-222-2220000-2-2-200-2-2220000-2-2222000000-2-22-2202-22-200000000000000000000000000
χ33222-22-2-2-222-2-2-2000022-20022-2-200000000-2002i2i−2i−2i2-2200000002i−2i2i−2i002i−2i000000000000000000
χ34222-22-2-2-222-2-2-2000022-20022-2-200000000-200−2i−2i2i2i2-220000000−2i2i−2i2i00−2i2i000000000000000000
χ35222-22-2-2-222-2-2-2000022-200-2-22200000000-2002i2i−2i−2i22-20000000−2i2i−2i2i002i−2i000000000000000000
χ36222-22-2-2-222-2-2-2000022-200-2-22200000000-200−2i−2i2i2i22-200000002i−2i2i−2i00−2i2i000000000000000000
χ37222-22-2-2-2-2-22220000-2-220000002i2i−2i−2i22-2-2-2000000200-22000002i−2i−2i2i2i−2i00000000000000000000
χ38222-22-2-2-2-2-22220000-2-220000002i2i−2i−2i-2-222-20000002002-200000−2i2i2i−2i2i−2i00000000000000000000
χ39222-22-2-2-2-2-22220000-2-22000000−2i−2i2i2i22-2-2-2000000200-2200000−2i2i2i−2i−2i2i00000000000000000000
χ40222-22-2-2-2-2-22220000-2-22000000−2i−2i2i2i-2-222-20000002002-2000002i−2i−2i2i−2i2i00000000000000000000
χ41222-22-2-2-2-2-22-2-200002220000002i2i−2i−2i00002002i2i−2i−2i-2000002-2-220000−2i2i−2i2i000000000000000000
χ42222-22-2-2-2-2-22-2-200002220000002i2i−2i−2i0000200−2i−2i2i2i-200000-222-20000−2i2i2i−2i000000000000000000
χ43222-22-2-2-2-2-22-2-20000222000000−2i−2i2i2i00002002i2i−2i−2i-200000-222-200002i−2i−2i2i000000000000000000
χ44222-22-2-2-2-2-22-2-20000222000000−2i−2i2i2i0000200−2i−2i2i2i-2000002-2-2200002i−2i2i−2i000000000000000000
χ4522-2-2-222-20002-22i2i−2i−2i2-202i−2i000000002i−2i2i−2i0002-22-2000000000000000000i2i2−i2−i222−2−200002−2i2−i200
χ4622-2-2-222-20002-22i2i−2i−2i2-202i−2i000000002i−2i2i−2i0002-22-2000000000000000000−i2−i2i2i2−2−2220000−22−i2i200
χ4722-2-2-222-20002-22i2i−2i−2i2-202i−2i00000000−2i2i−2i2i000-22-22000000000000000000i2i2−i2−i222−2−20000−22−i2i200
χ4822-2-2-222-20002-22i2i−2i−2i2-202i−2i00000000−2i2i−2i2i000-22-22000000000000000000−i2−i2i2i2−2−22200002−2i2−i200
χ4922-2-2-222-20002-2−2i−2i2i2i2-20−2i2i000000002i−2i2i−2i000-22-22000000000000000000i2i2−i2−i2−2−22200002−2−i2i200
χ5022-2-2-222-20002-2−2i−2i2i2i2-20−2i2i000000002i−2i2i−2i000-22-22000000000000000000−i2−i2i2i222−2−20000−22i2−i200
χ5122-2-2-222-20002-2−2i−2i2i2i2-20−2i2i00000000−2i2i−2i2i0002-22-2000000000000000000i2i2−i2−i2−2−2220000−22i2−i200
χ5222-2-2-222-20002-2−2i−2i2i2i2-20−2i2i00000000−2i2i−2i2i0002-22-2000000000000000000−i2−i2i2i222−2−200002−2−i2i200
χ532-22-2-2-2222-22002-22-200-2002i−2i2i−2i2i−2i2i−2i000002-20000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−2000000
χ542-22-2-2-2222-22002-22-200-2002i−2i2i−2i2i−2i2i−2i000002-20000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22000000
χ552-22-2-2-2222-22002-22-200-200−2i2i−2i2i−2i2i−2i2i000002-20000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22000000
χ562-22-2-2-2222-22002-22-200-200−2i2i−2i2i−2i2i−2i2i000002-20000000000000000000000−i2i2−i2i2−i2i2−i2i22−22−2000000
χ572-22-2-2-2222-2200-22-2200-2002i−2i2i−2i−2i2i−2i2i00000-220000000000000000000000i2−i2i2−i2−i2i2−i2i22−2−22000000
χ582-22-2-2-2222-2200-22-2200-2002i−2i2i−2i−2i2i−2i2i00000-220000000000000000000000−i2i2−i2i2i2−i2i2−i2−222−2000000
χ592-22-2-2-2222-2200-22-2200-200−2i2i−2i2i2i−2i2i−2i00000-220000000000000000000000i2−i2i2−i2−i2i2−i2i2−222−2000000
χ602-22-2-2-2222-2200-22-2200-200−2i2i−2i2i2i−2i2i−2i00000-220000000000000000000000−i2i2−i2i2i2−i2i2−i22−2−22000000
χ6144-44-4-4-440004-40000-44000000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ6244-44-4-4-440004-40000-4400000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ6344-44-4-4-44000-4400004-40000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ6444-44-4-4-44000-4400004-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ6544-4-4-444-4000-444i4i−4i−4i-440−4i4i0000000000000000000000000000000000000000000000000000000
χ6644-4-4-444-4000-44−4i−4i4i4i-4404i−4i0000000000000000000000000000000000000000000000000000000
χ674-444-44-4-44-4-4000000004004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ684-444-44-4-44-4-400000000400−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ694-444-44-4-4-44400000000-40000004-4-4400000000000000000000000000000000000000000000000
χ704-444-44-4-4-44400000000-4000000-444-400000000000000000000000000000000000000000000000
χ714-44-4-4-444-44-4004-44-4004000000000000000-440000000000000000000000000000000000000000
χ724-44-4-4-444-44-400-44-440040000000000000004-40000000000000000000000000000000000000000
χ734-4-444-44-4000004i−4i−4i4i0000000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ744-4-444-44-4000004i−4i−4i4i000000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ754-4-444-44-400000−4i4i4i−4i0000000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ764-4-444-44-400000−4i4i4i−4i000000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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