Finite Group Databasebeta

← Group #274698

Character table — Group #274698

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444444444448888888844444888888888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-222-2-22-2-2-2-2222222-2-2-2-200000000-222-2-2000000000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-222-2-2-2-2222200000000-2-2-222000000000000000000000000000000
χ19222222222222-222-2-222-222-2-2-2-20000000022222222-200000000-2-2-2-20000000000000000000000
χ20222222222222-222-2-222-222-2-2-2-200000000-2-2-2-2-2-2-2-2-20000000022220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-2000000000000000020000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-200000000000000002000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2322222222-2-2-2-22-2-222-2-2222-2-2-2-22222-2-2-2-2000000002-2-222000000000000000000000000000000
χ2422222222-2-2-2-22-2-222-2-2222-2-2-2-2-2-2-2-2222200000000222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-2-2-222000000002222-2-2-2-2200000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-2-2-22200000000-2-2-2-2222220000000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ292222-2-2-2-222-2-20-2-2002202-20000000000002i2i−2i−2i2i2i−2i−2i0000022−2−200000000000022−2−20000i2−i2i2−i200
χ302222-2-2-2-222-2-20-2-2002202-20000000000002i2i−2i−2i2i2i−2i−2i00000−2−222000000000000−2−2220000−i2i2−i2i200
χ312222-2-2-2-222-2-20-2-2002202-2000000000000−2i−2i2i2i−2i−2i2i2i0000022−2−200000000000022−2−20000−i2i2−i2i200
χ322222-2-2-2-222-2-20-2-2002202-2000000000000−2i−2i2i2i−2i−2i2i2i00000−2−222000000000000−2−2220000i2−i2i2−i200
χ332222-2-2-2-2-2-2220-2-200220-220000000000002i2i−2i−2i−2i−2i2i2i0000022−2−2000000000000−2−2220000i2−i2−i2i200
χ342222-2-2-2-2-2-2220-2-200220-220000000000002i2i−2i−2i−2i−2i2i2i00000−2−22200000000000022−2−20000−i2i2i2−i200
χ352222-2-2-2-2-2-2220-2-200220-22000000000000−2i−2i2i2i2i2i−2i−2i0000022−2−2000000000000−2−2220000−i2i2i2−i200
χ362222-2-2-2-2-2-2220-2-200220-22000000000000−2i−2i2i2i2i2i−2i−2i00000−2−22200000000000022−2−20000i2−i2−i2i200
χ3722-2-22-22-22i−2i2i−2i200-2-200200002i−2i00002i2i−2i−2i2−22−2i2−i2i2−i20002-200002−2i2−i2i2−i2i2−i22−22−200000000000000
χ3822-2-22-22-22i−2i2i−2i200-2-200200002i−2i00002i2i−2i−2i−22−22−i2i2−i2i20002-20000−22−i2i2−i2i2−i2i2−22−2200000000000000
χ3922-2-22-22-22i−2i2i−2i200-2-200200002i−2i0000−2i−2i2i2i2−22−2i2−i2i2−i2000-2200002−2i2−i2−i2i2−i2i2−22−2200000000000000
χ4022-2-22-22-22i−2i2i−2i200-2-200200002i−2i0000−2i−2i2i2i−22−22−i2i2−i2i2000-220000−22−i2i2i2−i2i2−i22−22−200000000000000
χ4122-2-22-22-22i−2i2i−2i-2002200-20000−2i2i22-2-200002−22−2i2−i2i2−i202i−2i000000−22−i2i22−2−22−i2i2i2−i200000000000000
χ4222-2-22-22-22i−2i2i−2i-2002200-20000−2i2i22-2-20000−22−22−i2i2−i2i202i−2i0000002−2i2−i2−222−2i2−i2−i2i200000000000000
χ4322-2-22-22-22i−2i2i−2i-2002200-20000−2i2i-2-22200002−22−2i2−i2i2−i20−2i2i000000−22−i2i2−222−2i2−i2−i2i200000000000000
χ4422-2-22-22-22i−2i2i−2i-2002200-20000−2i2i-2-2220000−22−22−i2i2−i2i20−2i2i0000002−2i2−i22−2−22−i2i2i2−i200000000000000
χ4522-2-22-22-2−2i2i−2i2i200-2-20020000−2i2i00002i2i−2i−2i2−22−2−i2i2−i2i2000-2200002−2−i2i2i2−i2i2−i2−22−2200000000000000
χ4622-2-22-22-2−2i2i−2i2i200-2-20020000−2i2i00002i2i−2i−2i−22−22i2−i2i2−i2000-220000−22i2−i2−i2i2−i2i22−22−200000000000000
χ4722-2-22-22-2−2i2i−2i2i200-2-20020000−2i2i0000−2i−2i2i2i2−22−2−i2i2−i2i20002-200002−2−i2i2−i2i2−i2i22−22−200000000000000
χ4822-2-22-22-2−2i2i−2i2i200-2-20020000−2i2i0000−2i−2i2i2i−22−22i2−i2i2−i20002-20000−22i2−i2i2−i2i2−i2−22−2200000000000000
χ4922-2-22-22-2−2i2i−2i2i-2002200-200002i−2i22-2-200002−22−2−i2i2−i2i20−2i2i000000−22i2−i22−2−22i2−i2−i2i200000000000000
χ5022-2-22-22-2−2i2i−2i2i-2002200-200002i−2i22-2-20000−22−22i2−i2i2−i20−2i2i0000002−2−i2i2−222−2−i2i2i2−i200000000000000
χ5122-2-22-22-2−2i2i−2i2i-2002200-200002i−2i-2-22200002−22−2−i2i2−i2i202i−2i000000−22i2−i2−222−2−i2i2i2−i200000000000000
χ5222-2-22-22-2−2i2i−2i2i-2002200-200002i−2i-2-2220000−22−22i2−i2i2−i202i−2i0000002−2−i2i22−2−22i2−i2−i2i200000000000000
χ532-22-2-2-222000022-22-22-2-2002-2002-22-22-22-2000000000000000000000000000002i−2i2i−2i002i−2i000000
χ542-22-2-2-222000022-22-22-2-2002-2002-22-22-22-200000000000000000000000000000−2i2i−2i2i00−2i2i000000
χ552-22-2-2-222000022-22-22-2-2002-200-22-22-22-22000000000000000000000000000002i−2i2i−2i00−2i2i000000
χ562-22-2-2-222000022-22-22-2-2002-200-22-22-22-2200000000000000000000000000000−2i2i−2i2i002i−2i000000
χ572-22-2-2-22200002-222-2-22-200-22002-22-2-22-2200000000000002i−2i2i−2i00000000000000002i−2i00000000
χ582-22-2-2-22200002-222-2-22-200-22002-22-2-22-220000000000000−2i2i−2i2i0000000000000000−2i2i00000000
χ592-22-2-2-22200002-222-2-22-200-2200-22-222-22-200000000000002i−2i2i−2i0000000000000000−2i2i00000000
χ602-22-2-2-22200002-222-2-22-200-2200-22-222-22-20000000000000−2i2i−2i2i00000000000000002i−2i00000000
χ614444-4-4-4-444-4-404400-4-40-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-44404400-4-404-40000000000000000000000000000000000000000000000000000000
χ6344-4-4-44-444i−4i−4i4i00000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000
χ6444-4-4-44-444i−4i−4i4i0000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000
χ6544-4-4-44-44−4i4i4i−4i00000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000
χ6644-4-4-44-44−4i4i4i−4i0000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000
χ674-44-444-4-4000004-400-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ684-44-444-4-4000004-400-440000000000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ694-44-444-4-400000-44004-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ704-44-444-4-400000-44004-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ714-44-4-4-4440000-44-4-444-4400-4400000000000000000000000000000000000000000000000000000
χ724-44-4-4-4440000-4-44-44-444004-400000000000000000000000000000000000000000000000000000
χ734-4-44-444-40000400-4400-400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ744-4-44-444-40000400-4400-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ754-4-44-444-40000-4004-40040000004-4-4400000000000000000000000000000000000000000000000
χ764-4-44-444-40000-4004-4004000000-444-400000000000000000000000000000000000000000000000
χ778-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000

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