Finite Group Databasebeta

← Group #243469

Character table — Group #243469

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444444444444888888888888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-11-1-1-1-11111111-1-111-1-111-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-1-1-11111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-11111-1-1
χ1111111111-1-1-1-11-1-1-1-11111111-1-111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111
χ1211111111-1-1-1-11-1-1-1-11111111-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ1311111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1
χ1611111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-222-2-2222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-222-2-2222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ19222222222222-2222222-2-222-2-2-2-2-2-2-200000000222200000000-2-2-2-200000000000000000000
χ20222222222222-2222222-2-222-2-2-2-2-2-2-200000000-2-2-2-200000000222200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-2-2-222222-2-222-2-22-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-222222-2-222-2-22-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-2-2-2-222-2-222-222-2-2220000000022-2-200000000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-222-2-222-222-2-22200000000-2-2220000000022-2-200000000000000000000
χ29222-2-22-2-222-2-2022-2-2-2-200220000000000000002i−2i2i−2ii2i2−i2−i222−2−20000i2i2−i2−i222−2−2000000000000
χ30222-2-22-2-222-2-2022-2-2-2-200220000000000000002i−2i2i−2i−i2−i2i2i2−2−2220000−i2−i2i2i2−2−222000000000000
χ31222-2-22-2-222-2-2022-2-2-2-20022000000000000000−2i2i−2i2ii2i2−i2−i2−2−2220000i2i2−i2−i2−2−222000000000000
χ32222-2-22-2-222-2-2022-2-2-2-20022000000000000000−2i2i−2i2i−i2−i2i2i222−2−20000−i2−i2i2i222−2−2000000000000
χ33222-2-22-2-2-2-2220-2-222-2-200220000000000000002i−2i−2i2ii2i2−i2−i222−2−20000−i2−i2i2i2−2−222000000000000
χ34222-2-22-2-2-2-2220-2-222-2-200220000000000000002i−2i−2i2i−i2−i2i2i2−2−2220000i2i2−i2−i222−2−2000000000000
χ35222-2-22-2-2-2-2220-2-222-2-20022000000000000000−2i2i2i−2ii2i2−i2−i2−2−2220000−i2−i2i2i222−2−2000000000000
χ36222-2-22-2-2-2-2220-2-222-2-20022000000000000000−2i2i2i−2i−i2−i2i2i222−2−20000i2i2−i2−i2−2−222000000000000
χ3722-22-2-22-22i−2i2i−2i02i−2i2i−2i2-2002-20000000000000000000i2−i2i2−i2i2−i2i2−i22-22i−2i2−22−22−22−2000000000000
χ3822-22-2-22-22i−2i2i−2i02i−2i2i−2i2-2002-20000000000000000000i2−i2i2−i2−i2i2−i2i2-22−2i2i2−22−2−22−22000000000000
χ3922-22-2-22-22i−2i2i−2i02i−2i2i−2i2-2002-20000000000000000000−i2i2−i2i2i2−i2i2−i2-22−2i2i−22−222−22−2000000000000
χ4022-22-2-22-22i−2i2i−2i02i−2i2i−2i2-2002-20000000000000000000−i2i2−i2i2−i2i2−i2i22-22i−2i−22−22−22−22000000000000
χ4122-22-2-22-2−2i2i−2i2i0−2i2i−2i2i2-2002-20000000000000000000i2−i2i2−i2i2−i2i2−i22-2−2i2i−22−22−22−22000000000000
χ4222-22-2-22-2−2i2i−2i2i0−2i2i−2i2i2-2002-20000000000000000000i2−i2i2−i2−i2i2−i2i2-222i−2i−22−222−22−2000000000000
χ4322-22-2-22-2−2i2i−2i2i0−2i2i−2i2i2-2002-20000000000000000000−i2i2−i2i2i2−i2i2−i2-222i−2i2−22−2−22−22000000000000
χ4422-22-2-22-2−2i2i−2i2i0−2i2i−2i2i2-2002-20000000000000000000−i2i2−i2i2−i2i2−i2i22-2−2i2i2−22−22−22−2000000000000
χ4522-2-22-2-222i−2i−2i2i22i−2i−2i2i-22-2-22-222i−2i2-22i−2i00000000000000002i−2i−2i2i000000002-2-22000000000000
χ4622-2-22-2-222i−2i−2i2i22i−2i−2i2i-22-2-22-222i−2i2-22i−2i0000000000000000−2i2i2i−2i00000000-222-2000000000000
χ4722-2-22-2-222i−2i−2i2i2−2i2i2i−2i2-2-2-2-2222i−2i-22−2i2i0000000000000000000000000000000000002i−2i2-20000
χ4822-2-22-2-222i−2i−2i2i2−2i2i2i−2i2-2-2-2-2222i−2i-22−2i2i000000000000000000000000000000000000−2i2i-220000
χ4922-2-22-2-222i−2i−2i2i-22i−2i−2i2i-22222-2-2−2i2i-22−2i2i0000000000002-2-2200000000−2i2i2i−2i0000000000000000
χ5022-2-22-2-222i−2i−2i2i-22i−2i−2i2i-22222-2-2−2i2i-22−2i2i000000000000-222-2000000002i−2i−2i2i0000000000000000
χ5122-2-22-2-222i−2i−2i2i-2−2i2i2i−2i2-222-22-2−2i2i2-22i−2i000000000000000000000000000000002-22i−2i00000000
χ5222-2-22-2-222i−2i−2i2i-2−2i2i2i−2i2-222-22-2−2i2i2-22i−2i00000000000000000000000000000000-22−2i2i00000000
χ5322-2-22-2-22−2i2i2i−2i22i−2i−2i2i2-2-2-2-222−2i2i-222i−2i0000000000000000000000000000000000002i−2i-220000
χ5422-2-22-2-22−2i2i2i−2i22i−2i−2i2i2-2-2-2-222−2i2i-222i−2i000000000000000000000000000000000000−2i2i2-20000
χ5522-2-22-2-22−2i2i2i−2i2−2i2i2i−2i-22-2-22-22−2i2i2-2−2i2i00000000000000002i−2i−2i2i00000000-222-2000000000000
χ5622-2-22-2-22−2i2i2i−2i2−2i2i2i−2i-22-2-22-22−2i2i2-2−2i2i0000000000000000−2i2i2i−2i000000002-2-22000000000000
χ5722-2-22-2-22−2i2i2i−2i-22i−2i−2i2i2-222-22-22i−2i2-2−2i2i000000000000000000000000000000002-2−2i2i00000000
χ5822-2-22-2-22−2i2i2i−2i-22i−2i−2i2i2-222-22-22i−2i2-2−2i2i00000000000000000000000000000000-222i−2i00000000
χ5922-2-22-2-22−2i2i2i−2i-2−2i2i2i−2i-22222-2-22i−2i-222i−2i0000000000002-2-22000000002i−2i−2i2i0000000000000000
χ6022-2-22-2-22−2i2i2i−2i-2−2i2i2i−2i-22222-2-22i−2i-222i−2i000000000000-222-200000000−2i2i2i−2i0000000000000000
χ61444-4-44-4-444-4-40-4-4444400-4-4000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-4-444044-4-44400-4-4000000000000000000000000000000000000000000000000000
χ6344-44-4-44-44i−4i4i−4i0−4i4i−4i4i-4400-44000000000000000000000000000000000000000000000000000
χ6444-44-4-44-4−4i4i−4i4i04i−4i4i−4i-4400-44000000000000000000000000000000000000000000000000000
χ654-4444-4-4-4000040000004-400-40000004-4000000000000000000000000000000000000000000
χ664-4444-4-4-4000040000004-400-4000000-44000000000000000000000000000000000000000000
χ674-4444-4-4-40000-4000000-4400400000000004i−4i00000000000000000000000000000000000000
χ684-4444-4-4-40000-4000000-440040000000000−4i4i00000000000000000000000000000000000000
χ694-4-4-4444-400004000000-4400-4000000004i−4i0000000000000000000000000000000000000000
χ704-4-4-4444-400004000000-4400-400000000−4i4i0000000000000000000000000000000000000000
χ714-4-4-4444-40000-40000004-40040000000000004-4000000000000000000000000000000000000
χ724-4-4-4444-40000-40000004-4004000000000000-44000000000000000000000000000000000000
χ738-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000

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