Finite Group Databasebeta

← Group #313884

Character table — Group #313884

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-111-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-111111-1-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-111-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-111-11
χ911111111111111111-1-1-1-1111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1111111-11-1-111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111-11-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-11-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-11-11111-1-1-11
χ17222222222-22-22-22-2-22222-200000000-2-2002200-2-22200000000-2-20000000000000000
χ18222222222-22-22-22-2-22222-200000000-2-200-2-20022-2-200000000220000000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000000022002200-2-2-2-200000000220000000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000000002200-2-200222200000000-2-20000000000000000
χ2122222222-22-22-22-22-20000-22222-2-2-2-2002200-2-2000000000000000000002-200000000
χ2222222222-22-22-22-22-20000-22222-2-2-2-200-2-2002200000000000000000000-2200000000
χ2322222222-22-22-22-22-20000-2-2-2-2-222220022002200000000000000000000-2-200000000
χ2422222222-22-22-22-22-20000-2-2-2-2-2222200-2-200-2-2000000000000000000002200000000
χ25222-22-2-2-220-20-202002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i2000000002i−2i0022−2−222−2−22-2i2i2−i2−i2000000000000
χ26222-22-2-2-220-20-202002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i200000000−2i2i00−2−22222−2−2-22−i2−i2i2i2000000000000
χ27222-22-2-2-220-20-202002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i2000000002i−2i00−2−222−2−2222-2−i2−i2i2i2000000000000
χ28222-22-2-2-220-20-202002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i200000000−2i2i0022−2−2−2−222-22i2i2−i2−i2000000000000
χ29222-22-2-2-220-20-20200−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i2000000002i−2i0022−2−2−2−222-22−i2−i2i2i2000000000000
χ30222-22-2-2-220-20-20200−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i200000000−2i2i00−2−222−2−2222-2i2i2−i2−i2000000000000
χ31222-22-2-2-220-20-20200−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i2000000002i−2i00−2−22222−2−2-22i2i2−i2−i2000000000000
χ32222-22-2-2-220-20-20200−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i200000000−2i2i0022−2−222−2−22-2−i2−i2i2i2000000000000
χ3322-22-2-22-222-2-222-2-2-22-22-222i−2i2i−2i2i−2i2i−2i2-2000000000000002i−2i2i−2i000000000000000000
χ3422-22-2-22-222-2-222-2-2-22-22-22−2i2i−2i2i−2i2i−2i2i2-200000000000000−2i2i−2i2i000000000000000000
χ3522-22-2-22-222-2-222-2-2-2-22-2222i−2i2i−2i2i−2i2i−2i-2200000000000000−2i2i−2i2i000000000000000000
χ3622-22-2-22-222-2-222-2-2-2-22-222−2i2i−2i2i−2i2i−2i2i-22000000000000002i−2i2i−2i000000000000000000
χ3722-22-2-22-22-2-222-2-2222-22-2-200000000-2200000000002i−2i2i−2i0000002i−2i2i−2i000000000000
χ3822-22-2-22-22-2-222-2-2222-22-2-200000000-220000000000−2i2i−2i2i000000−2i2i−2i2i000000000000
χ3922-22-2-22-22-2-222-2-222-22-22-2000000002-200000000002i−2i2i−2i000000−2i2i−2i2i000000000000
χ4022-22-2-22-22-2-222-2-222-22-22-2000000002-20000000000−2i2i−2i2i0000002i−2i2i−2i000000000000
χ4122-22-2-22-2-222-2-222-220000-22i−2i2i−2i−2i2i−2i2i000000000000000000000000002-2002i−2i000000
χ4222-22-2-22-2-222-2-222-220000-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000-2200−2i2i000000
χ4322-22-2-22-2-222-2-222-220000-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000002-200−2i2i000000
χ4422-22-2-22-2-222-2-222-220000-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000-22002i−2i000000
χ4522-2-2-22-222020-20-2002i−2i−2i2i02−2−222−2−2200002i−2i00002-2i2−i2−i2i2−i2i2i2−i200−222−2000000000000
χ4622-2-2-22-222020-20-2002i−2i−2i2i02−2−222−2−220000−2i2i0000-22−i2i2i2−i2−i2i2i2−i2002−2−22000000000000
χ4722-2-2-22-222020-20-2002i−2i−2i2i0−222−2−222−200002i−2i00002-2−i2i2i2−i2i2−i2−i2i2002−2−22000000000000
χ4822-2-2-22-222020-20-2002i−2i−2i2i0−222−2−222−20000−2i2i0000-22i2−i2−i2i2i2−i2−i2i200−222−2000000000000
χ4922-2-2-22-222020-20-200−2i2i2i−2i02−2−222−2−2200002i−2i0000-22i2−i2−i2i2i2−i2−i2i2002−2−22000000000000
χ5022-2-2-22-222020-20-200−2i2i2i−2i02−2−222−2−220000−2i2i00002-2−i2i2i2−i2i2−i2−i2i200−222−2000000000000
χ5122-2-2-22-222020-20-200−2i2i2i−2i0−222−2−222−200002i−2i0000-22−i2i2i2−i2−i2i2i2−i200−222−2000000000000
χ5222-2-2-22-222020-20-200−2i2i2i−2i0−222−2−222−20000−2i2i00002-2i2−i2−i2i2−i2i2i2−i2002−2−22000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-44-4-4-4-404040-400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ55444-44-4-4-4-404040-40000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-44-4-44-4-4-444-4-444-4000040000000000000000000000000000000000000000000000
χ5744-4-4-44-44-40-40404000000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-4-44-44-40-404040000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-44-4-444-404040-40-40000000000000000000000000000000000000000000000002i2−2i200
χ604-44-4-444-404040-40-4000000000000000000000000000000000000000000000000−2i22i200
χ614-44-4-444-40-40-4040400000000000000004-40000000000000000000000000000000000
χ624-44-4-444-40-40-404040000000000000000-440000000000000000000000000000000000
χ634-4-4-44-444040-40-404000000000000000000000000000000000000000000000022−220000
χ644-4-4-44-444040-40-4040000000000000000000000000000000000000000000000−22220000
χ654-4-4-44-4440-404040-4000000000000000000004-4000000000000000000000000000000
χ664-4-4-44-4440-404040-400000000000000000000-44000000000000000000000000000000
χ678-888-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8888-8-8000000000000000000000000000000000000000000000000000000000000

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