Finite Group Databasebeta

← Group #308451

Character table — Group #308451

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-11111-1-1-1
χ911111111111111111-1-1-1-111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-11-1-11-1-111-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-11111-1-1-1-1111111-1-1-1-11-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111111-1-1-1111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-111-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1111-1-1111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111111-1-1-1-1-11111-1
χ17222222222-2-2222-2-2-22222-20000-2-20000002222000000-2-200000000000-20000000
χ18222222222-2-2222-2-2-22222-20000-2-2000000-2-2-2-2000000220000000000020000000
χ19222222222-2-2222-2-2-2-2-2-2-2-200002200000022-2-20000002200000000000-20000000
χ20222222222-2-2222-2-2-2-2-2-2-2-2000022000000-2-222000000-2-20000000000020000000
χ2122222222-222-2-2-222-20000-222220022-2-2220000-2-200000000000000-20000000000
χ2222222222-222-2-2-222-20000-2222200-2-222-2-20000-2-20000000000000020000000000
χ2322222222-222-2-2-222-20000-2-2-2-2-20022-2-2-2-20000220000000000000020000000000
χ2422222222-222-2-2-222-20000-2-2-2-2-200-2-2222200002200000000000000-20000000000
χ25222-22-2-2-2222-22-2-2-2222-2-2-200002-200000000000000000000002-20000002-200000
χ26222-22-2-2-2222-22-2-2-2222-2-2-200002-20000000000000000000000-22000000-2200000
χ27222-22-2-2-2222-22-2-2-22-2-222-20000-2200000000000000000000002-2000000-2200000
χ28222-22-2-2-2222-22-2-2-22-2-222-20000-220000000000000000000000-220000002-200000
χ29222-22-2-2-22-2-2-22-222-222-2-220000-222i−2i2i−2i000000000000000000002i−2i00000000000
χ30222-22-2-2-22-2-2-22-222-222-2-220000-22−2i2i−2i2i00000000000000000000−2i2i00000000000
χ31222-22-2-2-22-2-2-22-222-2-2-222200002-22i−2i2i−2i00000000000000000000−2i2i00000000000
χ32222-22-2-2-22-2-2-22-222-2-2-222200002-2−2i2i−2i2i000000000000000000002i−2i00000000000
χ33222-22-2-2-2-2-2-22-222220000-20000002i−2i−2i2i0000000022-2-2000000000002i−2i00000000
χ34222-22-2-2-2-2-2-22-222220000-20000002i−2i−2i2i00000000-2-22200000000000−2i2i00000000
χ35222-22-2-2-2-2-2-22-222220000-2000000−2i2i2i−2i0000000022-2-200000000000−2i2i00000000
χ36222-22-2-2-2-2-2-22-222220000-2000000−2i2i2i−2i00000000-2-222000000000002i−2i00000000
χ3722-22-2-22-2200-2-220002i−2i2i−2i0i2i2−i2−i2000000002-22i−2ii2−i22−22−20022−2−20000000000i2−i2000
χ3822-22-2-22-2200-2-220002i−2i2i−2i0i2i2−i2−i200000000-22−2i2ii2−i22−22−200−2−2220000000000−i2i2000
χ3922-22-2-22-2200-2-220002i−2i2i−2i0−i2−i2i2i2000000002-22i−2i−i2i2−22−2200−2−2220000000000−i2i2000
χ4022-22-2-22-2200-2-220002i−2i2i−2i0−i2−i2i2i200000000-22−2i2i−i2i2−22−220022−2−20000000000i2−i2000
χ4122-22-2-22-2200-2-22000−2i2i−2i2i0i2i2−i2−i2000000002-2−2i2ii2−i2−22−2200−2−2220000000000i2−i2000
χ4222-22-2-22-2200-2-22000−2i2i−2i2i0i2i2−i2−i200000000-222i−2ii2−i2−22−220022−2−20000000000−i2i2000
χ4322-22-2-22-2200-2-22000−2i2i−2i2i0−i2−i2i2i2000000002-2−2i2i−i2i22−22−20022−2−20000000000−i2i2000
χ4422-22-2-22-2200-2-22000−2i2i−2i2i0−i2−i2i2i200000000-222i−2i−i2i22−22−200−2−2220000000000i2−i2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-4-4444-44-4-4-4000040000000000000000000000000000000000000000000
χ4744-44-4-44-4-40044-4000000002i22i2−2i2−2i2000000000000−2i22i20000000000000000000000000
χ4844-44-4-44-4-40044-400000000−2i2−2i22i22i20000000000002i2−2i20000000000000000000000000
χ4944-4-4-44-444004-4-40004i−4i−4i4i00000000000000000000000000000000000000000000
χ5044-4-4-44-444004-4-4000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5144-4-4-44-44-400-4440000000000000000000000000022−22−2222000000000000000000000
χ5244-4-4-44-44-400-44400000000000000000000000000−222222−22000000000000000000000
χ534-444-4-4-440000000000000022−2222−220000000000000000002i2−2i22i−2i2i−2i000000000000000
χ544-444-4-4-440000000000000022−2222−22000000000000000000−2i22i2−2i2i−2i2i000000000000000
χ554-444-4-4-4400000000000000−2222−22220000000000000000002i2−2i2−2i2i−2i2i000000000000000
χ564-444-4-4-4400000000000000−2222−2222000000000000000000−2i22i22i−2i2i−2i000000000000000
χ574-4-4444-4-404-40004-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ584-4-4444-4-404-40004-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ594-4-4444-4-40-44000-440000004i−4i−4i4i000000000000000000000000000000000000000
χ604-4-4444-4-40-44000-44000000−4i4i4i−4i000000000000000000000000000000000000000
χ614-4-4-44-44404-4000-4400000000000000004-40000000000000000000000000000000
χ624-4-4-44-44404-4000-440000000000000000-440000000000000000000000000000000
χ634-4-4-44-4440-440004-4000000000000000000000000000000000000000000000022−220
χ644-4-4-44-4440-440004-40000000000000000000000000000000000000000000000−22220
χ658-88-8-888-8000000000000000000000000000000000000000000000000000000000

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