Finite Group Databasebeta

← Group #293772

Character table — Group #293772

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444444444444888888888888888844444444444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-1-1-11-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-11-1-1-1-1-11-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1-1-1-11-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-1-1-1-1-111111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1111-1-1-1-111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-111-1-11111-1-1-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1-1111-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-11-1-111-1-111-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-1-1-11111-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-111-1-11111-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1111-111-1-111-1-1-11
χ1722222222222-2-2-2-2222-2-2-2-222-2-200000000000000002200-2-200200000-200000000000
χ1822222222222-2-2-2-2222-2-2-2-222-2-20000000000000000-2-2002200-200000200000000000
χ1922222222222-2-2-2-22-2-22222-2-2-2-200000000000000002200-2-200-200000200000000000
χ2022222222222-2-2-2-22-2-22222-2-2-2-20000000000000000-2-2002200200000-200000000000
χ2122222222-2-2-22222-222-2-222-2-2-2-20000000000000000002200220-200000-20000000000
χ2222222222-2-2-22222-222-2-222-2-2-2-2000000000000000000-2-200-2-2020000020000000000
χ2322222222-2-2-22222-2-2-222-2-222-2-20000000000000000002200-2-20200000-20000000000
χ2422222222-2-2-22222-2-2-222-2-222-2-2000000000000000000-2-200220-20000020000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000002-22-2000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000-22-22000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000-222-2000000000000
χ292-22-22-22-20002-22-202i−2i002i−2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2002-2002i−2i0000000000002−2i2−i200
χ302-22-22-22-20002-22-202i−2i002i−2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i200-2200−2i2i000000000000−22−i2i200
χ312-22-22-22-20002-22-202i−2i002i−2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i2002-2002i−2i000000000000−22−i2i200
χ322-22-22-22-20002-22-202i−2i002i−2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i200-2200−2i2i0000000000002−2i2−i200
χ332-22-22-22-20002-22-20−2i2i00−2i2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2002-200−2i2i0000000000002−2−i2i200
χ342-22-22-22-20002-22-20−2i2i00−2i2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i200-22002i−2i000000000000−22i2−i200
χ352-22-22-22-20002-22-20−2i2i00−2i2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i2002-200−2i2i000000000000−22i2−i200
χ362-22-22-22-20002-22-20−2i2i00−2i2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i200-22002i−2i0000000000002−2−i2i200
χ372-2-222-2-2222-22-2-22-2000000002-2000000002i2i−2i−2i2i2i−2i−2i2i−2i002i−2i0000000000002-2000000
χ382-2-222-2-2222-22-2-22-2000000002-2000000002i2i−2i−2i2i2i−2i−2i−2i2i00−2i2i000000000000-22000000
χ392-2-222-2-2222-22-2-22-2000000002-200000000−2i−2i2i2i−2i−2i2i2i2i−2i002i−2i000000000000-22000000
χ402-2-222-2-2222-22-2-22-2000000002-200000000−2i−2i2i2i−2i−2i2i2i−2i2i00−2i2i0000000000002-2000000
χ412-2-222-2-2222-2-222-2-200000000-222i2i−2i−2i2i2i−2i−2i000000002i−2i00−2i2i00000000002-200000000
χ422-2-222-2-2222-2-222-2-200000000-222i2i−2i−2i2i2i−2i−2i00000000−2i2i002i−2i0000000000-2200000000
χ432-2-222-2-2222-2-222-2-200000000-22−2i−2i2i2i−2i−2i2i2i000000002i−2i00−2i2i0000000000-2200000000
χ442-2-222-2-2222-2-222-2-200000000-22−2i−2i2i2i−2i−2i2i2i00000000−2i2i002i−2i00000000002-200000000
χ45444-4-4-4-4400000000004-40000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ46444-4-4-4-4400000000004-4000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ47444-4-4-4-440000000000-440000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ48444-4-4-4-440000000000-44000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ4944-44-4-44-44-440000-4000000000022−22−2222−222222−220000000000000000000000000000000000
χ5044-44-4-44-44-440000-40000000000−222222−2222−22−22220000000000000000000000000000000000
χ5144-44-4-44-4-44-4000040000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ5244-44-4-44-4-44-400004000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ5344-4-444-4-400044-4-400000000000000000002222−22−22−22−22222200000000000000000000000000
χ5444-4-444-4-400044-4-40000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5544-4-444-4-4000-4-444000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ5644-4-444-4-4000-4-44400000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ574-444-44-4-44-4-40000400000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ584-444-44-4-44-4-4000040000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ594-444-44-4-4-4440000-400000000000000000022−2222−22−2222−222200000000000000000000000000
χ604-444-44-4-4-4440000-4000000000000000000−2222−222222−2222−2200000000000000000000000000
χ614-44-44-44-4000-44-4404i−4i00−4i4i0000000000000000000000000000000000000000000000
χ624-44-44-44-4000-44-440−4i4i004i−4i0000000000000000000000000000000000000000000000
χ634-4-444-4-44-4-444-4-44400000000-44000000000000000000000000000000000000000000
χ644-4-444-4-44-4-44-444-44000000004-4000000000000000000000000000000000000000000
χ654-4-4-4-4444000000000000004-4002-2-222-2-222-2-222-2-2200000000000000000000000000
χ664-4-4-4-4444000000000000004-400-222-2-222-2-222-2-222-200000000000000000000000000
χ674-4-4-4-444400000000000000-44002-2-222-2-22-222-2-222-200000000000000000000000000
χ684-4-4-4-444400000000000000-4400-222-2-222-22-2-222-2-2200000000000000000000000000

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