Finite Group Databasebeta

← Group #256643

Character table — Group #256643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222244444444444444448888888888888888444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-1-11-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111
χ911111111-1-1-1-111111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11-1111-1-11111-1-1-1-111
χ1111111111-1-1-1-111111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-11111-1-1
χ1211111111-1-1-1-111111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-111
χ1311111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-11-111111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11-11-11111-1-111-1-1-1-111
χ1611111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1
χ1722222222222222-2-222-2-222-2-2-2-2-2-200000000000000000022002200000-2-2000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-2000000000000000000-2-200-2-20000022000000000000000
χ19222222222222-2-222-2-222-2-222-2-2-2-20000000000000000220022000000-200-200000000000000
χ20222222222222-2-222-2-222-2-222-2-2-2-20000000000000000-2-200-2-2000000200200000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000022-2-200002-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000-2-2220000-22000000000000
χ2322222222-2-2-2-222-2-222-2-2-2-222-222-20000000000000000002200-2-2000002-2000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-222-222-2000000000000000000-2-2002200000-22000000000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-222-200000000000000002200-2-2000000200-200000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-222-20000000000000000-2-20022000000-200200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2200000000000000000000000022-2-20000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-22000000000000000000000000-2-22200002-2000000000000
χ29222-2-2-22-222-2-200-2-20022002-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22i−2i002i−2i00000000000000002−22−20000
χ30222-2-2-22-222-2-200-2-20022002-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−2i2i00−2i2i0000000000000000−22−220000
χ31222-2-2-22-222-2-200-2-20022002-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i002i−2i0000000000000000−22−220000
χ32222-2-2-22-222-2-200-2-20022002-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i00−2i2i00000000000000002−22−20000
χ33222-2-2-22-2-2-22200-2-2002200-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22i−2i00−2i2i00000000000000002−2−220000
χ34222-2-2-22-2-2-22200-2-2002200-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−2i2i002i−2i0000000000000000−222−20000
χ35222-2-2-22-2-2-22200-2-2002200-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22i−2i00−2i2i0000000000000000−222−20000
χ36222-2-2-22-2-2-22200-2-2002200-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−2i2i002i−2i00000000000000002−2−220000
χ3722-22-2-2-222-22-2-2-20022002-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002-2002-2000000000000000000i2−i2i2−i2
χ3822-22-2-2-222-22-2-2-20022002-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200-2200-22000000000000000000−i2i2−i2i2
χ3922-22-2-2-222-22-2-2-20022002-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002-2002-2000000000000000000−i2i2−i2i2
χ4022-22-2-2-222-22-2-2-20022002-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200-2200-22000000000000000000i2−i2i2−i2
χ4122-22-2-2-22-22-22-2-2002200-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002-200-22000000000000000000i2−i2−i2i2
χ4222-22-2-2-22-22-22-2-2002200-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200-22002-2000000000000000000−i2i2i2−i2
χ4322-22-2-2-22-22-22-2-2002200-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002-200-22000000000000000000−i2i2i2−i2
χ4422-22-2-2-22-22-22-2-2002200-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200-22002-2000000000000000000i2−i2−i2i2
χ452-222-22-2-200002-22-22-22-20000-2002000000002-22-22-22-2000000002i−2i2i−2i000000002i−2i00000000
χ462-222-22-2-200002-22-22-22-20000-2002000000002-22-22-22-200000000−2i2i−2i2i00000000−2i2i00000000
χ472-222-22-2-200002-22-22-22-20000-200200000000-22-22-22-22000000002i−2i2i−2i00000000−2i2i00000000
χ482-222-22-2-200002-22-22-22-20000-200200000000-22-22-22-2200000000−2i2i−2i2i000000002i−2i00000000
χ492-222-22-2-20000-22-22-22-220000-20022-22-22-22-200000000000000002i−2i−2i2i0000002i−2i0000000000
χ502-222-22-2-20000-22-22-22-220000-20022-22-22-22-20000000000000000−2i2i2i−2i000000−2i2i0000000000
χ512-222-22-2-20000-22-22-22-220000-2002-22-22-22-2200000000000000002i−2i−2i2i000000−2i2i0000000000
χ522-222-22-2-20000-22-22-22-220000-2002-22-22-22-220000000000000000−2i2i2i−2i0000002i−2i0000000000
χ53444-4-4-44-444-4-4004400-4-400-4400000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-444004400-4-4004-400000000000000000000000000000000000000000000000000
χ5544-44-4-4-444-44-44400-4-400-440000000000000000000000000000000000000000000000000000
χ5644-44-4-4-44-44-444400-4-4004-40000000000000000000000000000000000000000000000000000
χ5744-4-444-4-44-4-44000000000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000
χ5844-4-444-4-44-4-440000000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000
χ5944-4-444-4-4-444-4000000000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000
χ6044-4-444-4-4-444-40000000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000
χ614-444-44-4-400004-4-444-4-440000400-40000000000000000000000000000000000000000000000
χ624-444-44-4-40000-444-4-444-40000400-40000000000000000000000000000000000000000000000
χ634-44-44-4-440000004-400-44000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ644-44-44-4-440000004-400-4400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ654-44-44-4-44000000-44004-400000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ664-44-44-4-44000000-44004-40000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ674-4-444-44-400004-400-4400000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ684-4-444-44-400004-400-440000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ694-4-444-44-40000-44004-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ704-4-444-44-40000-44004-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ714-4-4-4-4444000000000000000004-402-2-22-222-22-2-22-222-2000000000000000000000000000000
χ724-4-4-4-4444000000000000000004-40-222-22-2-22-222-22-2-22000000000000000000000000000000
χ734-4-4-4-444400000000000000000-4402-2-22-222-2-222-22-2-22000000000000000000000000000000
χ744-4-4-4-444400000000000000000-440-222-22-2-222-2-22-222-2000000000000000000000000000000

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