Finite Group Databasebeta

← Group #258992

Character table — Group #258992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1
χ911111111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-11-111-1-1-1-11-111-1-111-1-1
χ1011111111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-11111-1111-1-1-1-111
χ1111111111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1111-1-1-1-1-11-1-111-1-111
χ1211111111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1-111111-1-1-11111-1-1
χ1311111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1111111-1-11-1-1-1-1-1111-1-1-111-1-111
χ1411111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-11111-1-1-11-1-11111-1-1
χ1511111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-11-1-1-1-111-1111-1-111-1-1
χ1611111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-111111-1-11-111-1-1-1-111
χ17222222222222222-2-2-2-2222-2-2-2-2-2-20000000000000000222200000000-2-20000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-20000000000000000-2-2-2-200000000220000000000000000
χ1922222222222-2-2-2-2-2-2-2-22-2-22222-2-2000000000000000022-2-200000000-220000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-22222-2-20000000000000000-2-222000000002-20000000000000000
χ2122222222-2-2-222222222-2-2-222-2-2-2-2000000000000000000000000222200000000-2-200000000
χ2222222222-2-2-222222222-2-2-222-2-2-2-2000000000000000000000000-2-2-2-2000000002200000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-222220000000000000000000022-2-2000000002-2000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2222200000000000000000000-2-22200000000-22000000000000
χ2522222222-2-2-2-2-2-2-22222-222-2-222-2-200000000000000000000000022-2-200000000-2200000000
χ2622222222-2-2-2-2-2-2-22222-222-2-222-2-2000000000000000000000000-2-222000000002-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000022-2-200000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000-2-222000000002-2000000000000
χ292222-2-2-2-222-222-2-20000-22-20000002222−2−2−2−22222−2−2−2−22-22-20000000000000000002−22−20000
χ302222-2-2-2-222-222-2-20000-22-20000002222−2−2−2−22222−2−2−2−2-22-22000000000000000000−22−220000
χ312222-2-2-2-222-222-2-20000-22-2000000−2−2−2−22222−2−2−2−222222-22-2000000000000000000−22−220000
χ322222-2-2-2-222-222-2-20000-22-2000000−2−2−2−22222−2−2−2−22222-22-220000000000000000002−22−20000
χ332222-2-2-2-222-2-2-2220000-2-220000002222−2−2−2−2−2−2−2−222222-2-220000000000000000002−2−220000
χ342222-2-2-2-222-2-2-2220000-2-220000002222−2−2−2−2−2−2−2−22222-222-2000000000000000000−222−20000
χ352222-2-2-2-222-2-2-2220000-2-22000000−2−2−2−222222222−2−2−2−22-2-22000000000000000000−222−20000
χ362222-2-2-2-222-2-2-2220000-2-22000000−2−2−2−222222222−2−2−2−2-222-20000000000000000002−2−220000
χ3722-2-2-2-2222-220000-2-222-20000002-2000000002i2i−2i−2i2i2i−2i−2i00002i−2i2i−2i00000000002-20000000000
χ3822-2-2-2-2222-220000-2-222-20000002-2000000002i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i0000000000-220000000000
χ3922-2-2-2-2222-220000-2-222-20000002-200000000−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i0000000000-220000000000
χ4022-2-2-2-2222-220000-2-222-20000002-200000000−2i−2i2i2i−2i−2i2i2i0000−2i2i−2i2i00000000002-20000000000
χ4122-2-2-2-222-22-2000022-2-220000002-222-2-222-2-20000000000002i−2i−2i2i0000002i−2i00000000000000
χ4222-2-2-2-222-22-2000022-2-220000002-222-2-222-2-2000000000000−2i2i2i−2i000000−2i2i00000000000000
χ4322-2-2-2-222-22-2000022-2-220000002-2-2-222-2-2220000000000002i−2i−2i2i000000−2i2i00000000000000
χ4422-2-2-2-222-22-2000022-2-220000002-2-2-222-2-222000000000000−2i2i2i−2i0000002i−2i00000000000000
χ452-22-22-22-20002i−2i2i−2i2-22-20002i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000002-22i−2i00000000000000i2−i22−2
χ462-22-22-22-20002i−2i2i−2i2-22-20002i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000-22−2i2i00000000000000−i2i2−22
χ472-22-22-22-20002i−2i2i−2i2-22-20002i−2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000002-22i−2i00000000000000−i2i2−22
χ482-22-22-22-20002i−2i2i−2i2-22-20002i−2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000-22−2i2i00000000000000i2−i22−2
χ492-22-22-22-2000−2i2i−2i2i2-22-2000−2i2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000002-2−2i2i00000000000000i2−i2−22
χ502-22-22-22-2000−2i2i−2i2i2-22-2000−2i2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000-222i−2i00000000000000−i2i22−2
χ512-22-22-22-2000−2i2i−2i2i2-22-2000−2i2i0000−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000002-2−2i2i00000000000000−i2i22−2
χ522-22-22-22-2000−2i2i−2i2i2-22-2000−2i2i0000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000-222i−2i00000000000000i2−i2−22
χ534444-4-4-4-4-4-4444-4-400004-440000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-44-4-444000044-40000000000000000000000000000000000000000000000000000
χ5544-4-444-4-44-4-400000000400000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000
χ5644-4-444-4-44-4-40000000040000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000
χ5744-4-444-4-4-44400000000-4000000002222−22−22−22−22222200000000000000000000000000000000000000
χ5844-4-444-4-4-44400000000-400000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5944-4-4-4-4444-44000044-4-4-4000000-440000000000000000000000000000000000000000000000
χ6044-4-4-4-444-44-40000-4-4444000000-440000000000000000000000000000000000000000000000
χ614-44-44-44-40004i−4i4i−4i-44-44000−4i4i00000000000000000000000000000000000000000000000000
χ624-44-44-44-4000−4i4i−4i4i-44-440004i−4i00000000000000000000000000000000000000000000000000
χ634-44-4-44-440004i−4i−4i4i00000000000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000000000
χ644-44-4-44-440004i−4i−4i4i0000000000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000000000
χ654-44-4-44-44000−4i4i4i−4i00000000000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000000000
χ664-44-4-44-44000−4i4i4i−4i0000000000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000000000
χ674-4-444-4-4400000000000000004-4002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ684-4-444-4-4400000000000000004-400−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ694-4-444-4-440000000000000000-44002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ704-4-444-4-440000000000000000-4400−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ714-4-44-444-400000004-4-440000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ724-4-44-444-400000004-4-44000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ734-4-44-444-40000000-444-4000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ744-4-44-444-40000000-444-400000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000

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