Finite Group Databasebeta

← Group #307482

Character table — Group #307482

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-111111-1-11-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1
χ111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-111-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-111-1-11-1-1111-1
χ1722222222222-2-2-2-220000-2-22222-2-2-2-222000022000000000000000000-20000-2000000
χ1822222222222-2-2-2-220000-2-22222-2-2-2-2-2-20000-2-2000000000000000000200002000000
χ1922222222222-2-2-2-220000-2-2-2-2-2-22222220000-2-2000000000000000000-200002000000
χ2022222222222-2-2-2-220000-2-2-2-2-2-22222-2-200002200000000000000000020000-2000000
χ2122222222-2-2-22222-22222-2-2000000000022-2-200-2-222-2-2000000000000000000000000
χ2222222222-2-2-22222-22222-2-20000000000-2-22200-2-2-2-222000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2000000000022-2-20022-2-222000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-20000000000-2-222002222-2-2000000000000000000000000
χ2522-22-22-2-20002-22-2022-2-200i2i2−i2−i2i2i2−i2−i200002-20000002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-22-22-2-20002-22-2022-2-200i2i2−i2−i2i2i2−i2−i20000-22000000-22i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2722-22-22-2-20002-22-2022-2-200−i2−i2i2i2−i2−i2i2i200002-20000002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-22-22-2-20002-22-2022-2-200−i2−i2i2i2−i2−i2i2i20000-22000000-22−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2922-22-22-2-20002-22-20-2-22200i2i2−i2−i2i2i2−i2−i200002-2000000-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ3022-22-22-2-20002-22-20-2-22200i2i2−i2−i2i2i2−i2−i20000-220000002-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-22-22-2-20002-22-20-2-22200−i2−i2i2i2−i2−i2i2i200002-2000000-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3222-22-22-2-20002-22-20-2-22200−i2−i2i2i2−i2−i2i2i20000-220000002-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ332-222-2-22-20002-2-2202i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2002-20000002i−2i002−22−2i2−i2i2−i22−22−2000000000000
χ342-222-2-22-20002-2-2202i−2i2i−2i00i2−i2i2−i2i2−i2i2−i200-22000000−2i2i002−22−2−i2i2−i2i2−22−22000000000000
χ352-222-2-22-20002-2-2202i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2002-20000002i−2i00−22−22−i2i2−i2i2−22−22000000000000
χ362-222-2-22-20002-2-2202i−2i2i−2i00−i2i2−i2i2−i2i2−i2i200-22000000−2i2i00−22−22i2−i2i2−i22−22−2000000000000
χ372-222-2-22-20002-2-220−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2002-2000000−2i2i00−22−22i2−i2i2−i2−22−22000000000000
χ382-222-2-22-20002-2-220−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i200-220000002i−2i00−22−22−i2i2−i2i22−22−2000000000000
χ392-222-2-22-20002-2-220−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2002-2000000−2i2i002−22−2−i2i2−i2i22−22−2000000000000
χ402-222-2-22-20002-2-220−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i200-220000002i−2i002−22−2i2−i2i2−i2−22−22000000000000
χ412-2-222-2-222-2-222-2-222i−2i−2i2i2-200000000000000002i−2i000000002-2-22−2i2i2i−2i000000000000
χ422-2-222-2-222-2-222-2-222i−2i−2i2i2-200000000000000002i−2i00000000-222-22i−2i−2i2i000000000000
χ432-2-222-2-222-2-222-2-22−2i2i2i−2i2-20000000000000000−2i2i000000002-2-222i−2i−2i2i000000000000
χ442-2-222-2-222-2-222-2-22−2i2i2i−2i2-20000000000000000−2i2i00000000-222-2−2i2i2i−2i000000000000
χ452-2-222-2-22-22222-2-2-22i−2i−2i2i-222-2-222-2-2200000000−2i2i0000−2i2i2i−2i00000000000000000000
χ462-2-222-2-22-22222-2-2-22i−2i−2i2i-22-222-2-222-200000000−2i2i00002i−2i−2i2i00000000000000000000
χ472-2-222-2-22-22222-2-2-2−2i2i2i−2i-222-2-222-2-22000000002i−2i00002i−2i−2i2i00000000000000000000
χ482-2-222-2-22-22222-2-2-2−2i2i2i−2i-22-222-2-222-2000000002i−2i0000−2i2i2i−2i00000000000000000000
χ492-2-222-2-22-222-2-222-200002-22-2-22-222-20000000000000000000000000002i−2i2i−2i0000000
χ502-2-222-2-22-222-2-222-200002-22-2-22-222-2000000000000000000000000000−2i2i−2i2i0000000
χ512-2-222-2-22-222-2-222-200002-2-222-22-2-220000000000000000000000000002i−2i−2i2i0000000
χ522-2-222-2-22-222-2-222-200002-2-222-22-2-22000000000000000000000000000−2i2i2i−2i0000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-44-4-4-444-40000-4000000000000004-4000000000000000000000000000000000000
χ55444-44-4-4-444-40000-400000000000000-44000000000000000000000000000000000000
χ56444-44-4-4-4-4-440000400000000000000000000000000000000000000000000002i2−2i20000
χ57444-44-4-4-4-4-44000040000000000000000000000000000000000000000000000−2i22i20000
χ5844-44-44-4-4000-44-4400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5944-44-44-4-4000-44-440000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ604-444-4-44-4000-444-400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ614-444-4-44-4000-444-40000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ624-4-444-4-444-4-4-4-44440000-440000000000000000000000000000000000000000000000
χ634-4-4-4444-44-440000-40000000000000000000000000000000000000000000000002i2−2i200
χ644-4-4-4444-44-440000-4000000000000000000000000000000000000000000000000−2i22i200
χ654-4-4-4444-4-44-400004000000000000000000004-4000000000000000000000000000000
χ664-4-4-4444-4-44-40000400000000000000000000-44000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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