Finite Group Databasebeta

← Group #308396

Character table — Group #308396

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-11-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111
χ71111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-111-1-111-1
χ911111111111111111-1-1-1-111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ1011111111111111111-1-1-1-111111-1-1111111-1-1111111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-11111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-111111-1-1-1-111-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-111-1-111-1-11111-1
χ17222222222-2-22-222-2-22222-20000-2-200000022-2-22200000000000-20000000000000
χ18222222222-2-22-222-2-22222-20000-2-2000000-2-222-2-20000000000020000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-20000220000002222-2-200000000000-20000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000022000000-2-2-2-2220000000000020000000000000
χ2122222222-222-22-2-22-20000-222220022-2-2-2-2000000-2-200000000200000000000000
χ2222222222-222-22-2-22-20000-2222200-2-22222000000-2-200000000-200000000000000
χ2322222222-222-22-2-22-20000-2-2-2-2-20022-2-2220000002200000000-200000000000000
χ2422222222-222-22-2-22-20000-2-2-2-2-200-2-222-2-20000002200000000200000000000000
χ25222-2-2-2-22-200202-2002i2i−2i−2i0i2i2−i2−i2000000002-2002i−2ii2−i222−2−222−2−2000000000000i2−i20
χ26222-2-2-2-22-200202-2002i2i−2i−2i0i2i2−i2−i200000000-2200−2i2ii2−i222−2−2−2−222000000000000−i2i20
χ27222-2-2-2-22-200202-2002i2i−2i−2i0−i2−i2i2i2000000002-2002i−2i−i2i2−2−222−2−222000000000000−i2i20
χ28222-2-2-2-22-200202-2002i2i−2i−2i0−i2−i2i2i200000000-2200−2i2i−i2i2−2−22222−2−2000000000000i2−i20
χ29222-2-2-2-22-200202-200−2i−2i2i2i0i2i2−i2−i2000000002-200−2i2ii2−i2−2−222−2−222000000000000i2−i20
χ30222-2-2-2-22-200202-200−2i−2i2i2i0i2i2−i2−i200000000-22002i−2ii2−i2−2−22222−2−2000000000000−i2i20
χ31222-2-2-2-22-200202-200−2i−2i2i2i0−i2−i2i2i2000000002-200−2i2i−i2i222−2−222−2−2000000000000−i2i20
χ32222-2-2-2-22-200202-200−2i−2i2i2i0−i2−i2i2i200000000-22002i−2i−i2i222−2−2−2−222000000000000i2−i20
χ332-222-22-2-2222-2-22-2-222-22-2-200002-20000000000000000000000002-200002-200000
χ342-222-22-2-2222-2-22-2-222-22-2-200002-2000000000000000000000000-220000-2200000
χ352-222-22-2-2222-2-22-2-22-22-22-20000-220000000000000000000000002-20000-2200000
χ362-222-22-2-2222-2-22-2-22-22-22-20000-22000000000000000000000000-2200002-200000
χ372-222-22-2-22-2-2-222-22-22-22-220000-222i−2i2i−2i0000000000000000000000002i−2i0000000
χ382-222-22-2-22-2-2-222-22-22-22-220000-22−2i2i−2i2i000000000000000000000000−2i2i0000000
χ392-222-22-2-22-2-2-222-22-2-22-22200002-22i−2i2i−2i000000000000000000000000−2i2i0000000
χ402-222-22-2-22-2-2-222-22-2-22-22200002-2−2i2i−2i2i0000000000000000000000002i−2i0000000
χ412-222-22-2-2-2-2-222-22220000-20000002i−2i−2i2i00000000002-22-2000000002i−2i000000000
χ422-222-22-2-2-2-2-222-22220000-20000002i−2i−2i2i0000000000-22-2200000000−2i2i000000000
χ432-222-22-2-2-2-2-222-22220000-2000000−2i2i2i−2i00000000002-22-200000000−2i2i000000000
χ442-222-22-2-2-2-2-222-22220000-2000000−2i2i2i−2i0000000000-22-22000000002i−2i000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-44400-40-4400000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ47444-4-4-4-44400-40-440000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ4844-444-4-4-40000000000000022−2222−22000000000022−22000000002-22-2000000000000000
χ4944-444-4-4-40000000000000022−2222−220000000000−222200000000-22-22000000000000000
χ5044-444-4-4-400000000000000−2222−2222000000000022−2200000000-22-22000000000000000
χ5144-444-4-4-400000000000000−2222−22220000000000−2222000000002-22-2000000000000000
χ5244-4-4-444-404-40400-400000000000000000000000000000022−22−2222000000000000000
χ5344-4-4-444-404-40400-4000000000000000000000000000000−222222−22000000000000000
χ5444-4-4-444-40-440-40040000004i−4i−4i4i000000000000000000000000000000000000000
χ5544-4-4-444-40-440-4004000000−4i4i4i−4i000000000000000000000000000000000000000
χ564-444-44-4-4-4444-4-44-4-4000040000000000000000000000000000000000000000000
χ574-44-44-44-440040-4-400000000000000000000000000022−22−22220000000000000000000
χ584-44-44-44-440040-4-4000000000000000000000000000−222222−220000000000000000000
χ594-44-44-44-4-400-4044004i−4i−4i4i00000000000000000000000000000000000000000000
χ604-44-44-44-4-400-404400−4i4i4i−4i00000000000000000000000000000000000000000000
χ614-4-4-444-4404-40-400400000000000000004-40000000000000000000000000000000
χ624-4-4-444-4404-40-40040000000000000000-440000000000000000000000000000000
χ634-4-4-444-440-440400-4000000000000000000000000000000000000000000002i2−2i2000
χ644-4-4-444-440-440400-400000000000000000000000000000000000000000000−2i22i2000
χ658-8-88-8-888000000000000000000000000000000000000000000000000000000000

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