Finite Group Databasebeta

← Group #329447

Character table — Group #329447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222222244444444444444444488888888888888884444444488888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-11-1-1-1-11111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-11-1-1-1-11111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-11-1-1-1-11111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-11-11
χ1211111111-1-1-1-11-1-1-1-11111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1111-11-1
χ1311111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-11-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222222-2-2-2-22-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ182222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-22222-222-2-2-2-200000000000000002222-2-2-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-22222-222-2-2-2-20000000000000000-2-2-2-2222200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-2-2-2-22-2-2-2-222-2-2-2-2222-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-22-2-2-2-222-2-2-2-2222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-22222-2-2-2-2-222000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-22222-2-22222-2-2-2-2-2220000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-22222-2-2-2-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-22222-2-2-2-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-222-2-2-222-2-2-222-2-22-20000200000000002i2i−2i−2i00002i2i−2i−2i0000000000000000i2−i2i2−i22−22−20000
χ3022-222-2-2-222-2-2-222-2-22-20000200000000002i2i−2i−2i00002i2i−2i−2i0000000000000000−i2i2−i2i2−22−220000
χ3122-222-2-2-222-2-2-222-2-22-2000020000000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000i2−i2i2−i2−22−220000
χ3222-222-2-2-222-2-2-222-2-22-2000020000000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000−i2i2−i2i22−22−20000
χ3322-222-2-2-2-2-222-2-2-2222-20000200000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000i2−i2−i2i22−2−220000
χ3422-222-2-2-2-2-222-2-2-2222-20000200000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000−i2i2i2−i2−222−20000
χ3522-222-2-2-2-2-222-2-2-2222-2000020000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000i2−i2−i2i2−222−20000
χ3622-222-2-2-2-2-222-2-2-2222-2000020000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000−i2i2i2−i22−2−220000
χ372-22-22-22-22-22-2000000022-2-202-20000i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i200002i−2i2i−2i2−22−22−22−2000000000000
χ382-22-22-22-22-22-2000000022-2-202-20000i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i20000−2i2i−2i2i−22−22−22−22000000000000
χ392-22-22-22-22-22-2000000022-2-202-20000−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i200002i−2i2i−2i−22−22−22−22000000000000
χ402-22-22-22-22-22-2000000022-2-202-20000−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i20000−2i2i−2i2i2−22−22−22−2000000000000
χ412-22-22-22-22-22-20000000-2-2220-220000i2i2−i2−i2−i2i2−i2i2i2i2−i2−i2−i2i2−i2i22-22-20000i2−i2−i2i2i2−i2−i2i2000000000000
χ422-22-22-22-22-22-20000000-2-2220-220000i2i2−i2−i2−i2i2−i2i2i2i2−i2−i2−i2i2−i2i2-22-220000−i2i2i2−i2−i2i2i2−i2000000000000
χ432-22-22-22-22-22-20000000-2-2220-220000−i2−i2i2i2i2−i2i2−i2−i2−i2i2i2i2−i2i2−i22-22-20000−i2i2i2−i2−i2i2i2−i2000000000000
χ442-22-22-22-22-22-20000000-2-2220-220000−i2−i2i2i2i2−i2i2−i2−i2−i2i2i2i2−i2i2−i2-22-220000i2−i2−i2i2i2−i2−i2i2000000000000
χ452-22-22-22-2-22-22000000022-2-20-220000i2i2−i2−i2i2−i2i2−i2−i2−i2i2i2−i2i2−i2i200002i−2i−2i2i2−22−2−22−22000000000000
χ462-22-22-22-2-22-22000000022-2-20-220000i2i2−i2−i2i2−i2i2−i2−i2−i2i2i2−i2i2−i2i20000−2i2i2i−2i−22−222−22−2000000000000
χ472-22-22-22-2-22-22000000022-2-20-220000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i2i2−i2i2−i200002i−2i−2i2i−22−222−22−2000000000000
χ482-22-22-22-2-22-22000000022-2-20-220000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i2i2−i2i2−i20000−2i2i2i−2i2−22−2−22−22000000000000
χ492-22-22-22-2-22-220000000-2-22202-20000i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2i2−i2i2−i22-2-220000i2−i2−i2i2−i2i2i2−i2000000000000
χ502-22-22-22-2-22-220000000-2-22202-20000i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2-222-20000−i2i2i2−i2i2−i2−i2i2000000000000
χ512-22-22-22-2-22-220000000-2-22202-20000−i2−i2i2i2i2−i2i2−i2i2i2−i2−i2−i2i2−i2i22-2-220000−i2i2i2−i2i2−i2−i2i2000000000000
χ522-22-22-22-2-22-220000000-2-22202-20000−i2−i2i2i2i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2-222-20000i2−i2−i2i2−i2i2i2−i2000000000000
χ53444-4-4-4-44000004i−4i4i−4i00000000000002i2−2i22i2−2i2000022−2222−2200000000000000000000000000000000
χ54444-4-4-4-44000004i−4i4i−4i0000000000000−2i22i2−2i22i20000−2222−222200000000000000000000000000000000
χ55444-4-4-4-4400000−4i4i−4i4i00000000000002i2−2i22i2−2i20000−2222−222200000000000000000000000000000000
χ56444-4-4-4-4400000−4i4i−4i4i0000000000000−2i22i2−2i22i2000022−2222−2200000000000000000000000000000000
χ5744-444-4-4-444-4-44-4-444-440000-400000000000000000000000000000000000000000000000000
χ5844-444-4-4-4-4-444444-4-4-440000-400000000000000000000000000000000000000000000000000
χ5944-4-4-444-4000004i−4i−4i4i004-44-4000004i−4i00000000000000000000000000000000000000000000
χ6044-4-4-444-4000004i−4i−4i4i00-44-4400000−4i4i00000000000000000000000000000000000000000000
χ6144-4-4-444-400000−4i4i4i−4i004-44-400000−4i4i00000000000000000000000000000000000000000000
χ6244-4-4-444-400000−4i4i4i−4i00-44-44000004i−4i00000000000000000000000000000000000000000000
χ634-444-44-4-40000400004-40000-40000004-4-440000000000000000000000000000000000000000
χ644-444-44-4-40000400004-40000-4000000-444-40000000000000000000000000000000000000000
χ654-444-44-4-40000-40000-4400004000000000000004i−4i−4i4i00000000000000000000000000000000
χ664-444-44-4-40000-40000-440000400000000000000−4i4i4i−4i00000000000000000000000000000000
χ674-4-44-4-444000040000-4-44-4-444004-40000000000000000000000000000000000000000000000
χ684-4-44-4-444000040000-4-4-444-4400-440000000000000000000000000000000000000000000000
χ694-4-44-4-4440000-40000444-4-44-400-440000000000000000000000000000000000000000000000
χ704-4-44-4-4440000-4000044-444-4-4004-40000000000000000000000000000000000000000000000
χ714-4-4-444-444-4-44000000000000000000000022−22−2222000022−22−22220000000000000000000000000000
χ724-4-4-444-444-4-440000000000000000000000−222222−220000−222222−220000000000000000000000000000
χ734-4-4-444-44-444-4000000000000000000000022−22−22220000−222222−220000000000000000000000000000
χ744-4-4-444-44-444-40000000000000000000000−222222−22000022−22−22220000000000000000000000000000

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