Finite Group Databasebeta

← Group #349474

Character table — Group #349474

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444422222244444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-111111111111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111-1-1-1-111-1-11-1-11111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111111111-1-1-1-111-1-11-1-11111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111111111-1-1-1-111-1-11-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1111111-1-1-1-111-1-1-1-111-11
χ1211111111111111-1-1-1-111-1-11-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-111-1-1-1-11111-1-11111-1-11-1
χ1311111111111111-1-1-1-111-1-11-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111111111-1-1-1-111-1-11-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ1511111111111111-1-1-1-111-1-11-1-1-1-1-1-11111-1-1-1-111111-1-11111-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ1611111111111111-1-1-1-111-1-11-1-1-1-1-1-11111-1-1-1-111111-1-11111-1-111-1-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-2-222222-222-2-2-22222222200000000-2-2-2000000-2-20000-200000000000000000000
χ1822222222222-2-2-222222-222-2-2-2-2-2-2-2-2-2-2-200000000-222000000220000-200000000000000000000
χ1922222222222-2-2-2-2-2-2-22-2-2-2-2222222-2-2-2-200000000-2-2-2000000220000200000000000000000000
χ2022222222222-2-2-2-2-2-2-22-2-2-2-222-2-2-2-2222200000000-222000000-2-20000200000000000000000000
χ2122222222-2-2-22222222-22-2-2-2220000000022222222-2000000-2-2000000-2-2-2000000000000000000
χ2222222222-2-2-22222222-22-2-2-22200000000-2-2-2-2-2-2-2-2-200000022000000-222000000000000000000
χ2322222222-2-2-2222-2-2-2-2-2222-2-2-2000000002222-2-2-2-2-2000000-2-2000000222000000000000000000
χ2422222222-2-2-2222-2-2-2-2-2222-2-2-200000000-2-2-2-22222-2000000220000002-2-2000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-22-2-2000000000000000020022-2-2000022-2-2200000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-22-2-20000000000000000200-2-2220000-2-222200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222000000000000000020022-2-20000-2-222-200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222220000000000000000200-2-222000022-2-2-200000000000000000000
χ29222-2-2-22-22-2-200022-2-2202-20002i2i−2i−2i2i2i−2i−2i00000000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ30222-2-2-22-22-2-200022-2-2202-20002i2i−2i−2i2i2i−2i−2i00000000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ31222-2-2-22-22-2-200022-2-2202-2000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ32222-2-2-22-22-2-200022-2-2202-2000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ33222-2-2-22-22-2-2000-2-22220-220002i2i−2i−2i−2i−2i2i2i00000000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ34222-2-2-22-22-2-2000-2-22220-220002i2i−2i−2i−2i−2i2i2i00000000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ35222-2-2-22-22-2-2000-2-22220-22000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ36222-2-2-22-22-2-2000-2-22220-22000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ3722-222-2-2-222-222-20000-2-2002002-22-2000022-2-20000-22-22-22-22-2000000000000000000000000000
χ3822-222-2-2-222-222-20000-2-2002002-22-20000-2-2220000-22-2-22-22-22000000000000000000000000000
χ3922-222-2-2-222-222-20000-2-200200-22-22000022-2-20000-2-22-22-222-2000000000000000000000000000
χ4022-222-2-2-222-222-20000-2-200200-22-220000-2-2220000-2-222-22-2-22000000000000000000000000000
χ4122-222-2-2-222-2-2-220000-2200-2002-22-2000000002i2i−2i−2i2-22000000002i−2i2i−2i02i−2i000000000000000000
χ4222-222-2-2-222-2-2-220000-2200-2002-22-200000000−2i−2i2i2i2-2200000000−2i2i−2i2i0−2i2i000000000000000000
χ4322-222-2-2-222-2-2-220000-2200-200-22-22000000002i2i−2i−2i22-200000000−2i2i−2i2i02i−2i000000000000000000
χ4422-222-2-2-222-2-2-220000-2200-200-22-2200000000−2i−2i2i2i22-2000000002i−2i2i−2i0−2i2i000000000000000000
χ4522-222-2-2-2-2-2222-200002-200-20000002i−2i2i−2i22-2-200002000000-222i−2i2i−2i−2i2i000000000000000000000
χ4622-222-2-2-2-2-2222-200002-200-20000002i−2i2i−2i-2-222000020000002-22i−2i−2i2i2i−2i000000000000000000000
χ4722-222-2-2-2-2-2222-200002-200-2000000−2i2i−2i2i22-2-200002000000-22−2i2i−2i2i2i−2i000000000000000000000
χ4822-222-2-2-2-2-2222-200002-200-2000000−2i2i−2i2i-2-222000020000002-2−2i2i2i−2i−2i2i000000000000000000000
χ4922-222-2-2-2-2-22-2-220000220020000002i−2i2i−2i00002i2i−2i−2i-2002-2-2200−2i2i00000−2i2i000000000000000000
χ5022-222-2-2-2-2-22-2-220000220020000002i−2i2i−2i0000−2i−2i2i2i-200-222-200−2i2i000002i−2i000000000000000000
χ5122-222-2-2-2-2-22-2-22000022002000000−2i2i−2i2i00002i2i−2i−2i-200-222-2002i−2i00000−2i2i000000000000000000
χ5222-222-2-2-2-2-22-2-22000022002000000−2i2i−2i2i0000−2i−2i2i2i-2002-2-22002i−2i000002i−2i000000000000000000
χ532-2-2-2222-20002-222-22-20-20002-2000000002-22-22-22-2000000000000000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i200
χ542-2-2-2222-20002-222-22-20-20002-2000000002-22-22-22-2000000000000000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i200
χ552-2-2-2222-20002-222-22-20-20002-200000000-22-22-22-22000000000000000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i200
χ562-2-2-2222-20002-222-22-20-20002-200000000-22-22-22-22000000000000000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i200
χ572-2-2-2222-20002-22-22-220-2000-22000000002-22-2-22-22000000000000000000i2−i2i2−i2−i2i2−i2i20000i2−i2−i2i200
χ582-2-2-2222-20002-22-22-220-2000-22000000002-22-2-22-22000000000000000000−i2i2−i2i2i2−i2i2−i20000−i2i2i2−i200
χ592-2-2-2222-20002-22-22-220-2000-2200000000-22-222-22-2000000000000000000i2−i2i2−i2−i2i2−i2i20000−i2i2i2−i200
χ602-2-2-2222-20002-22-22-220-2000-2200000000-22-222-22-2000000000000000000−i2i2−i2i2i2−i2i2−i20000i2−i2−i2i200
χ61444-4-4-44-4-44400044-4-4-40-440000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-444000-4-444-404-40000000000000000000000000000000000000000000000000000000
χ6344-4-4-44-444-440000000-40000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ6444-4-4-44-444-440000000-4000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ6544-4-4-44-44-44-40000000400000000004-4-4400000000000000000000000000000000000000000000
χ6644-4-4-44-44-44-4000000040000000000-444-400000000000000000000000000000000000000000000
χ674-44-44-4-440004-4-400000400000000000004-4-440000000000000000000000000000000000000000
χ684-44-44-4-440004-4-40000040000000000000-444-40000000000000000000000000000000000000000
χ694-44-44-4-44000-44400000-4000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ704-44-44-4-44000-44400000-400000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ714-4-44-4-4440000004-4-44000000000000000000000000000000000000000002-2-222-2-220000000000
χ724-4-44-4-4440000004-4-4400000000000000000000000000000000000000000-222-2-222-20000000000
χ734-4-44-4-444000000-444-4000000000000000000000000000000000000000002-2-22-222-20000000000
χ744-4-44-4-444000000-444-400000000000000000000000000000000000000000-222-22-2-220000000000
χ754-4-4-4444-4000-44-44-44-404000-440000000000000000000000000000000000000000000000000000
χ764-4-4-4444-4000-44-4-44-44040004-40000000000000000000000000000000000000000000000000000
χ778-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000

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