Finite Group Databasebeta

← Group #256659

Character table — Group #256659

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222244444444444444448888888888888888224444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-11-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111
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
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-11-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-11-1-111111111-1-1-1-1
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
χ911111111-1-1-1-111111111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ1011111111-1-1-1-111111111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1-1-11111-1-1-1-111
χ1111111111-1-1-1-111111111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-11-1-1-1-111-1-11111-1-1
χ1211111111-1-1-1-111111111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111
χ1311111111-1-1-1-111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1411111111-1-1-1-111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-111-1-1-111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-111111-1-11-1-111-1-111-1-1-1-111
χ1611111111-1-1-1-111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1
χ1722222222222222-2-222-2-222-2-2-2-2-2-20000000000000000220022000000-20-2000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-20000000000000000-2-200-2-2000000202000000000000000
χ19222222222222-2-222-2-222-2-2-2-2-222-200000000000000000022002200000-20-200000000000000
χ20222222222222-2-222-2-222-2-2-2-2-222-2000000000000000000-2-200-2-20000020200000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2222-2-2200000000000000000000000022-2-200002-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2222-2-22000000000000000000000000-2-2220000-22000000000000
χ2322222222-2-2-2-222-2-222-2-2-2-2-22222-200000000000000002200-2-200000020-2000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-2-22222-20000000000000000-2-20022000000-202000000000000000
χ2522222222-2-2-2-2-2-222-2-22222-222-2-2-20000000000000000002200-2-20000020-200000000000000
χ2622222222-2-2-2-2-2-222-2-22222-222-2-2-2000000000000000000-2-2002200000-20200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-222200000000000000000000000022-2-20000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2222000000000000000000000000-2-22200002-2000000000000
χ29222-2-2-22-222-2-2-2-20022002-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22-2002-20000000000000000i2−i2i2−i20000
χ30222-2-2-22-222-2-2-2-20022002-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2200-220000000000000000−i2i2−i2i20000
χ31222-2-2-22-222-2-2-2-20022002-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22-2002-20000000000000000−i2i2−i2i20000
χ32222-2-2-22-222-2-2-2-20022002-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-2200-220000000000000000i2−i2i2−i20000
χ33222-2-2-22-2-2-222-2-2002200-22000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22-200-220000000000000000i2−i2−i2i20000
χ34222-2-2-22-2-2-222-2-2002200-22000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-22002-20000000000000000−i2i2i2−i20000
χ35222-2-2-22-2-2-222-2-2002200-22000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22-200-220000000000000000−i2i2i2−i20000
χ36222-2-2-22-2-2-222-2-2002200-22000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-22002-20000000000000000i2−i2−i2i20000
χ372-222-22-2-200002-22-22-22-200-2000020000000022-2-222-2-2000000002i−2i2i−2i0000002i−2i0000000000
χ382-222-22-2-200002-22-22-22-200-2000020000000022-2-222-2-200000000−2i2i−2i2i000000−2i2i0000000000
χ392-222-22-2-200002-22-22-22-200-20000200000000-2-222-2-222000000002i−2i2i−2i000000−2i2i0000000000
χ402-222-22-2-200002-22-22-22-200-20000200000000-2-222-2-22200000000−2i2i−2i2i0000002i−2i0000000000
χ412-222-22-2-20000-22-22-22-2200-20000222-2-222-2-200000000000000002i−2i−2i2i000000002i−2i00000000
χ422-222-22-2-20000-22-22-22-2200-20000222-2-222-2-20000000000000000−2i2i2i−2i00000000−2i2i00000000
χ432-222-22-2-20000-22-22-22-2200-200002-2-222-2-22200000000000000002i−2i−2i2i00000000−2i2i00000000
χ442-222-22-2-20000-22-22-22-2200-200002-2-222-2-2220000000000000000−2i2i2i−2i000000002i−2i00000000
χ452-2-2-2222-22-22-2002200-2-2000002-20i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i0000000000000000002−22−2
χ462-2-2-2222-22-22-2002200-2-2000002-20i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i000000000000000000−22−22
χ472-2-2-2222-22-22-2002200-2-2000002-20−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i000000000000000000−22−22
χ482-2-2-2222-22-22-2002200-2-2000002-20−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i0000000000000000002−22−2
χ492-2-2-2222-2-22-22002200-2-200000-220i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2002i−2i00−2i2i0000000000000000002−2−22
χ502-2-2-2222-2-22-22002200-2-200000-220i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200−2i2i002i−2i000000000000000000−222−2
χ512-2-2-2222-2-22-22002200-2-200000-220−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2002i−2i00−2i2i000000000000000000−222−2
χ522-2-2-2222-2-22-22002200-2-200000-220−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200−2i2i002i−2i0000000000000000002−2−22
χ53444-4-4-44-444-4-44400-4-400-440000000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-4444400-4-4004-40000000000000000000000000000000000000000000000000000
χ5544-444-4-4-40000000000000004-40002-2-22-222-22-2-22-222-2000000000000000000000000000000
χ5644-444-4-4-40000000000000004-4000-222-22-2-22-222-22-2-22000000000000000000000000000000
χ5744-444-4-4-4000000000000000-440002-2-22-222-2-222-22-2-22000000000000000000000000000000
χ5844-444-4-4-4000000000000000-44000-222-22-2-222-2-22-222-2000000000000000000000000000000
χ5944-4-4-44-440000004-400-4400000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ6044-4-4-44-440000004-400-440000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ6144-4-4-44-44000000-44004-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ6244-4-4-44-44000000-44004-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ634-444-44-4-400004-4-444-4-440040000-40000000000000000000000000000000000000000000000
χ644-444-44-4-40000-444-4-444-40040000-40000000000000000000000000000000000000000000000
χ654-44-44-4-4400004-400-4400000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ664-44-44-4-4400004-400-440000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ674-44-44-4-440000-44004-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000
χ684-44-44-4-440000-44004-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000
χ694-4-44-4-4444-4-4400000000000000002-22-2-22-222-22-2-22-22000000000000000000000000000000
χ704-4-44-4-4444-4-440000000000000000-22-222-22-2-22-222-22-2000000000000000000000000000000
χ714-4-44-4-444-444-400000000000000002-22-2-22-22-22-222-22-2000000000000000000000000000000
χ724-4-44-4-444-444-40000000000000000-22-222-22-22-22-2-22-22000000000000000000000000000000
χ734-4-4-4444-44-44-400-4-4004400000-4400000000000000000000000000000000000000000000000
χ744-4-4-4444-4-44-4400-4-40044000004-400000000000000000000000000000000000000000000000

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