Finite Group Databasebeta

← Group #10712421

Character table — Group #10712421

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222223444466666888812121212242424242222161616162424484848484848484844442466666612124444881616161688
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ91111-1-1111-1-1111-1-11-11-11-1-11111111-1-111-1-1-1-11111-1-1-1-1ii−i−i1-111-1-111-1-1ii−i−ii−iii−i−ii−i
χ101111-1-1111-1-1111-1-11-11-11-1-11111111-1-111-1-1-1-11111-1-1-1-1−i−iii1-111-1-111-1-1−i−iii−ii−i−iii−ii
χ111111-1-1111-1-1111-1-11-11-11-1-11111111-1-1-1-111-1-1-1-1-1-11111ii−i−i-1111-1-1-1-111ii−i−ii−i−i−iii−ii
χ121111-1-1111-1-1111-1-11-11-11-1-11111111-1-1-1-111-1-1-1-1-1-11111−i−iii-1111-1-1-1-111−i−iii−iiii−i−ii−i
χ131111-1-1111-1-1111-1-11-11-11-1-111111-1-11111-1-1-1-11111-1-1-1-1ii−i−i-11-1-111-1-111−i−iiii−iii−i−i−ii
χ141111-1-1111-1-1111-1-11-11-11-1-111111-1-11111-1-1-1-11111-1-1-1-1−i−iii-11-1-111-1-111ii−i−i−ii−i−iiii−i
χ151111-1-1111-1-1111-1-11-11-11-1-111111-1-111-1-111-1-1-1-1-1-11111ii−i−i1-1-1-11111-1-1−i−iiii−i−i−iiii−i
χ161111-1-1111-1-1111-1-11-11-11-1-111111-1-111-1-111-1-1-1-1-1-11111−i−iii1-1-1-11111-1-1ii−i−i−iiii−i−i−ii
χ172222222222222222-2-2-2-22222-2-2-2-200000000-2-200000000222200000000000000-2-2000000
χ182222222222222222-2-2-2-22222-2-2-2-200000000-2-200000000-2-2-2-20000000000000022000000
χ19222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ21222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ22222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ232222-2-2222-2-2222-2-2-22-222-2-22-2-2-2-20000000022000000002i2i−2i−2i00000000000000−2i2i000000
χ242222-2-2222-2-2222-2-2-22-222-2-22-2-2-2-2000000002200000000−2i−2i2i2i000000000000002i−2i000000
χ252222-2-2-122-2-2-1-1-1112-22-2-111-1-1-1-1-122-2-222-2-211-1-1-1-1111100002-2-1-111-1-111000000000000
χ262222-2-2-122-2-2-1-1-1112-22-2-111-1-1-1-1-122-2-2-2-222111111-1-1-1-10000-22-1-11111-1-1000000000000
χ272222-2-2-122-2-2-1-1-1112-22-2-111-1-1-1-1-1-2-22222-2-211-1-1-1-111110000-2211-1-111-1-1000000000000
χ282222-2-2-122-2-2-1-1-1112-22-2-111-1-1-1-1-1-2-222-2-222111111-1-1-1-100002-211-1-1-1-111000000000000
χ292-2-222-222-22-2-2-222-2000022-2-2000000002−22−20022−2−222−2−22i−2i2i−2i0000000000000000−i2i2−i2i200
χ302-2-222-222-22-2-2-222-2000022-2-2000000002−22−20022−2−222−2−2−2i2i−2i2i0000000000000000i2−i2i2−i200
χ312-2-222-222-22-2-2-222-2000022-2-200000000−22−2200−2−222−2−2222i−2i2i−2i0000000000000000i2−i2i2−i200
χ322-2-222-222-22-2-2-222-2000022-2-200000000−22−2200−2−222−2−222−2i2i−2i2i0000000000000000−i2i2−i2i200
χ332-2-222-22-22-22-2-222-222-2-2-2-22222-2-2000000002-200000000000000000000002i−2i2i−2i00000000
χ342-2-222-22-22-22-2-222-222-2-2-2-22222-2-2000000002-20000000000000000000000−2i2i−2i2i00000000
χ352-2-222-22-22-22-2-222-2-2-222-2-222-2-2222-22-20000-22000000000000002-22-20000000000000000
χ362-2-222-22-22-22-2-222-2-2-222-2-222-2-222-22-220000-2200000000000000-22-220000000000000000
χ372-2-222-2-1-22-2211-1-11-2-22211-1-111-1-12-22-200001-1−i3i3−i3i3−i3i3−i3i3000000-11-11−i3i3−i3i3000000000000
χ382-2-222-2-1-22-2211-1-11-2-22211-1-111-1-12-22-200001-1i3−i3i3−i3i3−i3i3−i3000000-11-11i3−i3i3−i3000000000000
χ392-2-222-2-1-22-2211-1-11-2-22211-1-111-1-1-22-2200001-1−i3i3−i3i3−i3i3−i3i30000001-11-1i3−i3i3−i3000000000000
χ402-2-222-2-1-22-2211-1-11-2-22211-1-111-1-1-22-2200001-1i3−i3i3−i3i3−i3i3−i30000001-11-1−i3i3−i3i3000000000000
χ412-2-22-2222-2-22-2-22-2200002-22-2000000002−2−220022−2−2−2−2222-2-220000000000000000−222−200
χ422-2-22-2222-2-22-2-22-2200002-22-2000000002−2−220022−2−2−2−222-222-200000000000000002−2−2200
χ432-2-22-2222-2-22-2-22-2200002-22-200000000−222−200−2−22222−2−22-2-2200000000000000002−2−2200
χ442-2-22-2222-2-22-2-22-2200002-22-200000000−222−200−2−22222−2−2-222-20000000000000000−222−200
χ452-2-22-222-222-2-2-22-222-2-22-22-2222-2-200000000-2200000000000000000000002-2-2200000000
χ462-2-22-222-222-2-2-22-222-2-22-22-2222-2-200000000-220000000000000000000000-222-200000000
χ472-2-22-222-222-2-2-22-22-222-2-22-22-2-2222-2-2200002-2000000000000002-2-220000000000000000
χ482-2-22-222-222-2-2-22-22-222-2-22-22-2-222-222-200002-200000000000000-222-20000000000000000
χ492-2-22-22-1-222-211-11-1-222-21-11-111-1-12-2-220000-11−i3i3−i3i3i3−i3i3−i3000000-111-1−i3i3i3−i3000000000000
χ502-2-22-22-1-222-211-11-1-222-21-11-111-1-12-2-220000-11i3−i3i3−i3−i3i3−i3i3000000-111-1i3−i3−i3i3000000000000
χ512-2-22-22-1-222-211-11-1-222-21-11-111-1-1-222-20000-11−i3i3−i3i3i3−i3i3−i30000001-1-11i3−i3−i3i3000000000000
χ522-2-22-22-1-222-211-11-1-222-21-11-111-1-1-222-20000-11i3−i3i3−i3−i3i3−i3i30000001-1-11−i3i3i3−i3000000000000
χ534444444-4-4-4-4444440000-4-4-4-4000000000000000000000000000000000000000000000000
χ54444444-24444-2-2-2-2-2-4-4-4-4-2-2-2-2222200000000220000000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-2-2-20000222200000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ56444444-2-4-4-4-4-2-2-2-2-20000222200000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ574444-4-44-4-444444-4-40000-444-4000000000000000000000000000000000000000000000000
χ584444-4-4-244-4-4-2-2-222-44-44-222-2222200000000-2-20000000000000000000000000000000000
χ594444-4-4-2-4-444-2-2-22200002-2-2200000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ604444-4-4-2-4-444-2-2-22200002-2-2200000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ614-4-444-4-24-44-422-2-220000-2-2220000000022−2222−2200−2−222−2−22200000000000000000000000000
χ624-4-444-4-24-44-422-2-220000-2-22200000000−2222−22220022−2−222−2−200000000000000000000000000
χ634-4-444-4-2-44-4422-2-2244-4-422-2-2-2-22200000000-220000000000000000000000000000000000
χ644-4-44-44-24-4-4422-22-20000-22-220000000022−22−222200−2−22222−2−200000000000000000000000000
χ654-4-44-44-24-4-4422-22-20000-22-2200000000−222222−220022−2−2−2−22200000000000000000000000000
χ664-4-44-44-2-444-422-22-24-4-442-22-2-2-222000000002-20000000000000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-44400000000002i6−2i62i6−2i600000000000000000000000000000000000000000000
χ6988-8-800-40000-4440000000000−2i62i6−2i62i600000000000000000000000000000000000000000000
χ708-88-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ718-88-800-400004-4400000000002i6−2i6−2i62i600000000000000000000000000000000000000000000
χ728-88-800-400004-440000000000−2i62i62i6−2i600000000000000000000000000000000000000000000

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