Finite Group Databasebeta

← Group #242037

Character table — Group #242037

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222444444444444444444448888888888888888888888882444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-11-1-1-1-1-1-1-11-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-111-1-1-1-11-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ911111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1-111111-1-11-1-1-1
χ1011111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-111-1-1-111-1-1-1111
χ1111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1111111
χ1211111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-11111-1-111-1-1-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-111-1-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-111-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-111-11111-1-1-11-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1-11-1-111-1-11-111
χ1722222222222222-2-222-2-2-2-222-2-2-2-20000000000000000000000002200-20000000-2000
χ1822222222222222-2-222-2-2-2-222-2-2-2-2000000000000000000000000-2-200200000002000
χ19222222222222-2-222-2-222-2-2-2-222-2-200000000000000000000000000220-20000000-200
χ20222222222222-2-222-2-222-2-2-2-222-2-200000000000000000000000000-2-2020000000200
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000002-22-20000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000-22-220000
χ2322222222-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000002-20020000000-2000
χ2422222222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000-2200-200000002000
χ2522222222-2-2-2-2-2-222-2-2222222-2-2-2-2000000000000000000000000002-20-20000000200
χ2622222222-2-2-2-2-2-222-2-2222222-2-2-2-200000000000000000000000000-22020000000-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000000000-222-20000
χ2922-2-22-22-22i2i−2i−2i2-22-22-22-22i−2i2i−2i2i−2i2-2000000000000000022-2-22i2i−2i−2i0000000000000000
χ3022-2-22-22-22i2i−2i−2i2-22-22-22-22i−2i2i−2i2i−2i2-20000000000000000-2-222−2i−2i2i2i0000000000000000
χ3122-2-22-22-22i2i−2i−2i2-2-222-2-22−2i2i2i−2i−2i2i-222i2i−2i−2i22-2-200000000000000000000000000000000
χ3222-2-22-22-22i2i−2i−2i2-2-222-2-22−2i2i2i−2i−2i2i-22−2i−2i2i2i-2-22200000000000000000000000000000000
χ3322-2-22-22-22i2i−2i−2i-222-2-222-2−2i2i−2i2i2i−2i-220000000022-2-22i2i−2i−2i000000000000000000000000
χ3422-2-22-22-22i2i−2i−2i-222-2-222-2−2i2i−2i2i2i−2i-2200000000-2-222−2i−2i2i2i000000000000000000000000
χ3522-2-22-22-22i2i−2i−2i-22-22-22-222i−2i−2i2i−2i2i2-20000000000000000000000000000002-20000002i−2i
χ3622-2-22-22-22i2i−2i−2i-22-22-22-222i−2i−2i2i−2i2i2-2000000000000000000000000000000-22000000−2i2i
χ3722-2-22-22-2−2i−2i2i2i2-22-22-22-2−2i2i−2i2i−2i2i2-2000000000000000022-2-2−2i−2i2i2i0000000000000000
χ3822-2-22-22-2−2i−2i2i2i2-22-22-22-2−2i2i−2i2i−2i2i2-20000000000000000-2-2222i2i−2i−2i0000000000000000
χ3922-2-22-22-2−2i−2i2i2i2-2-222-2-222i−2i−2i2i2i−2i-222i2i−2i−2i-2-22200000000000000000000000000000000
χ4022-2-22-22-2−2i−2i2i2i2-2-222-2-222i−2i−2i2i2i−2i-22−2i−2i2i2i22-2-200000000000000000000000000000000
χ4122-2-22-22-2−2i−2i2i2i-222-2-222-22i−2i2i−2i−2i2i-220000000022-2-2−2i−2i2i2i000000000000000000000000
χ4222-2-22-22-2−2i−2i2i2i-222-2-222-22i−2i2i−2i−2i2i-2200000000-2-2222i2i−2i−2i000000000000000000000000
χ4322-2-22-22-2−2i−2i2i2i-22-22-22-22−2i2i2i−2i2i−2i2-20000000000000000000000000000002-2000000−2i2i
χ4422-2-22-22-2−2i−2i2i2i-22-22-22-22−2i2i2i−2i2i−2i2-2000000000000000000000000000000-220000002i−2i
χ454444-4-4-4-44-44-4000000000000000000000000000000002-22-22-22-20000000000000000
χ464444-4-4-4-44-44-400000000000000000000000000000000-22-22-22-220000000000000000
χ474444-4-4-4-4-44-44000000000000000000000000000000002-22-2-22-220000000000000000
χ484444-4-4-4-4-44-4400000000000000000000000000000000-22-222-22-20000000000000000
χ4944-4-4-44-444i−4i−4i4i000000000000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ5044-4-4-44-444i−4i−4i4i00000000000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ5144-4-4-44-44−4i4i4i−4i000000000000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ5244-4-4-44-44−4i4i4i−4i00000000000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ534-44-444-4-400004400-4-4000000000022−2222−22000000000000000000000000000000000000
χ544-44-444-4-400004400-4-40000000000−2222−2222000000000000000000000000000000000000
χ554-44-444-4-40000-4-40044000000000000002i2−2i22i2−2i200000000000000000000000000000000
χ564-44-444-4-40000-4-4004400000000000000−2i22i2−2i22i200000000000000000000000000000000
χ574-44-4-4-4440000004400-4-400000000000000002i2−2i22i2−2i20000000000000000000000000000
χ584-44-4-4-4440000004400-4-40000000000000000−2i22i2−2i22i20000000000000000000000000000
χ594-44-4-4-444000000-4-400440000000000000000000022−2222−22000000000000000000000000
χ604-44-4-4-444000000-4-4004400000000000000000000−2222−2222000000000000000000000000
χ614-4-444-4-4400004-400-4400000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ624-4-444-4-4400004-400-440000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ634-4-444-4-440000-44004-4000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ644-4-444-4-440000-44004-400000000000000−2i22i22i2−2i200000000000000000000000000000000
χ654-4-44-444-40000004-400-4400000000000000002i2−2i2−2i22i20000000000000000000000000000
χ664-4-44-444-40000004-400-440000000000000000−2i22i22i2−2i20000000000000000000000000000
χ674-4-44-444-4000000-44004-4000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ684-4-44-444-4000000-44004-400000000000000000000−2i22i22i2−2i2000000000000000000000000

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