Finite Group Databasebeta

← Group #258936

Character table — Group #258936

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888444444444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-11-11-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-11-1-1-1-1-1-1-11-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11-11-1-11111-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-1-1-1111111111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-111-1-1-111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-111-1-111111-1-1-1-111
χ1111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-11-1-111-1-111
χ1211111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-111-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11-1-11111-1-11-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-11-1-1-1-111111-1-111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111111-1-1-111-1-1-1-111
χ1722222222222222-2-2-222-222-2-2-2-2-2-200000000000000000000002200220-20000000-200000000
χ1822222222222222-2-2-222-222-2-2-2-2-2-20000000000000000000000-2-200-2-2020000000200000000
χ19222222222222-2-2222-2-22-2-222-2-2-2-20000000000000000220000002200-20-2000000000000000
χ20222222222222-2-2222-2-22-2-222-2-2-2-20000000000000000-2-2000000-2-200202000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000022-2-20000000002-20000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000-2-222000000000-220000000000000
χ2322222222-2-2-2-222-2-2-222-2-2-22222-2-200000000000000000000002200-2-2020000000-200000000
χ2422222222-2-2-2-222-2-2-222-2-2-22222-2-20000000000000000000000-2-200220-20000000200000000
χ2522222222-2-2-2-2-2-2222-2-2222-2-222-2-2000000000000000022000000-2-200-202000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-222-2-20000000000000000-2-2000000220020-2000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000022-2-2000000000-220000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222000000000000000000-2-2220000000002-20000000000000
χ2922-22-22-2-222-2-2002-2-2002002-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22i−2i0000002i−2i0000000000002−22−20000
χ3022-22-22-2-222-2-2002-2-2002002-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−2i2i000000−2i2i000000000000−22−220000
χ3122-22-22-2-222-2-2002-2-2002002-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i0000002i−2i000000000000−22−220000
χ3222-22-22-2-222-2-2002-2-2002002-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i000000−2i2i0000000000002−22−20000
χ3322-22-22-2-2-2-222002-2-200200-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22i−2i000000−2i2i0000000000002−2−220000
χ3422-22-22-2-2-2-222002-2-200200-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−2i2i0000002i−2i000000000000−222−20000
χ3522-22-22-2-2-2-222002-2-200200-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22i−2i000000−2i2i000000000000−222−20000
χ3622-22-22-2-2-2-222002-2-200200-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−2i2i0000002i−2i0000000000002−2−220000
χ372-222-2-2-222i−2i2i−2i2-20002-202i−2i000000i2i2−i2−i2i2i2−i2−i222−2−222−2−20000002i−2i002-200000000000000i2−i22−2
χ382-222-2-2-222i−2i2i−2i2-20002-202i−2i000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000−2i2i00-2200000000000000−i2i2−22
χ392-222-2-2-222i−2i2i−2i2-20002-202i−2i000000−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000002i−2i002-200000000000000−i2i2−22
χ402-222-2-2-222i−2i2i−2i2-20002-202i−2i000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000−2i2i00-2200000000000000i2−i22−2
χ412-222-2-2-22−2i2i−2i2i2-20002-20−2i2i000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000002i−2i00-2200000000000000−i2i22−2
χ422-222-2-2-22−2i2i−2i2i2-20002-20−2i2i000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000−2i2i002-200000000000000i2−i2−22
χ432-222-2-2-22−2i2i−2i2i2-20002-20−2i2i000000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000002i−2i00-2200000000000000i2−i2−22
χ442-222-2-2-22−2i2i−2i2i2-20002-20−2i2i000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000−2i2i002-200000000000000−i2i22−2
χ452-22-2-222-2000022-22-2-2-220000002-22i−2i2i−2i2i−2i2i−2i00000000002i−2i2i−2i000000000002-200000000000
χ462-22-2-222-2000022-22-2-2-220000002-22i−2i2i−2i2i−2i2i−2i0000000000−2i2i−2i2i00000000000-2200000000000
χ472-22-2-222-2000022-22-2-2-220000002-2−2i2i−2i2i−2i2i−2i2i00000000002i−2i2i−2i00000000000-2200000000000
χ482-22-2-222-2000022-22-2-2-220000002-2−2i2i−2i2i−2i2i−2i2i0000000000−2i2i−2i2i000000000002-200000000000
χ492-22-2-222-20000-2-22-2222-20000002-2000000002-22-22-22-2002i−2i−2i2i00000000000002i−2i000000000
χ502-22-2-222-20000-2-22-2222-20000002-2000000002-22-22-22-200−2i2i2i−2i0000000000000−2i2i000000000
χ512-22-2-222-20000-2-22-2222-20000002-200000000-22-22-22-22002i−2i−2i2i0000000000000−2i2i000000000
χ522-22-2-222-20000-2-22-2222-20000002-200000000-22-22-22-2200−2i2i2i−2i00000000000002i−2i000000000
χ53444-44-4-4-400004-4000-4400000000022−22−222222−22−222200000000000000000000000000000000000000
χ54444-44-4-4-400004-4000-44000000000−222222−22−222222−2200000000000000000000000000000000000000
χ55444-44-4-4-40000-440004-40000000000000000022−22−222222−22−2222000000000000000000000000000000
χ56444-44-4-4-40000-440004-400000000000000000−222222−22−222222−22000000000000000000000000000000
χ5744-44-44-4-444-4-400-44400-400-4400000000000000000000000000000000000000000000000000
χ5844-44-44-4-4-4-44400-44400-4004-400000000000000000000000000000000000000000000000000
χ5944-4-4-4-44400000000000000004-4002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ6044-4-4-4-44400000000000000004-400−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ6144-4-4-4-4440000000000000000-44002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ6244-4-4-4-4440000000000000000-4400−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ634-444-4-4-444i−4i4i−4i-44000-440−4i4i0000000000000000000000000000000000000000000000000000
χ644-444-4-4-44−4i4i−4i4i-44000-4404i−4i0000000000000000000000000000000000000000000000000000
χ654-44-4-444-40000444-44-4-4-4000000-440000000000000000000000000000000000000000000000
χ664-44-4-444-40000-4-4-44-4444000000-440000000000000000000000000000000000000000000000
χ674-4-444-44-44i−4i−4i4i000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ684-4-444-44-44i−4i−4i4i0000000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ694-4-444-44-4−4i4i4i−4i000000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ704-4-444-44-4−4i4i4i−4i0000000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ714-4-4-444-4400000044-400-400000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ724-4-4-444-4400000044-400-40000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ734-4-4-444-44000000-4-440040000000022−2222−22−2222−222200000000000000000000000000000000000000
χ744-4-4-444-44000000-4-4400400000000−2222−222222−2222−2200000000000000000000000000000000000000

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