Finite Group Databasebeta

← Group #10697472

Character table — Group #10697472

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222444444448888888888888888161616161616161616161616242424242424242448484848
order122222344446666666444412121212888812121212242424242424242444441212121212121212888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-11
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-11
χ9222222222222222222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ10222222222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ112222222-2-2-2-222222222-22-2-2-2-2-2000022-2-200000000000000000000000022-2-20000
χ122222222-2-2-2-222222222-22-2-2-2-2-2000022-2-2000000000000000000000000-2-2220000
χ132222222-2-2-2-22222222-22-22-2-2-2-20000-2-2220000000000000000000022-2-200000000
χ142222222-2-2-2-22222222-22-22-2-2-2-20000-2-22200000000000000000000-2-22200000000
χ15222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-21111-1-1-1-1000000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222-1-1-1-11111000000000000
χ19222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ20222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000
χ232222-2-2222-2-2-2-222-2-2222-2-222-2-200002-22-200000000002i−2i2i−2i2i−2i0000000000000000
χ242222-2-2222-2-2-2-222-2-2222-2-222-2-200002-22-20000000000−2i2i−2i2i−2i2i0000000000000000
χ252222-2-2222-2-2-2-222-2-22-2-22222-2-20000-22-22000000002-20000002-22-2000000000000
χ262222-2-2222-2-2-2-222-2-22-2-22222-2-20000-22-2200000000-22000000-22-22000000000000
χ272222-2-22-2-222-2-222-2-222-2-22-2-22200002-2-220000000000000000000000000000200-2
χ282222-2-22-2-222-2-222-2-222-2-22-2-22200002-2-220000000000000000000000000000-2002
χ292222-2-22-2-222-2-222-2-22-222-2-2-2220000-222-2000000000000000000000000000002-20
χ302222-2-22-2-222-2-222-2-22-222-2-2-2220000-222-200000000000000000000000000000-220
χ312222-2-2-122-2-211-1-111-122-2-2-1-1110000-11-1133−3−333−3−3002i−2i−ii−ii−i3i3i3−i3000000000000
χ322222-2-2-122-2-211-1-111-122-2-2-1-1110000-11-1133−3−333−3−300−2i2ii−ii−ii3−i3−i3i3000000000000
χ332222-2-2-122-2-211-1-111-122-2-2-1-1110000-11-11−3−333−3−333002i−2i−ii−iii3−i3−i3i3000000000000
χ342222-2-2-122-2-211-1-111-122-2-2-1-1110000-11-11−3−333−3−33300−2i2ii−ii−i−i3i3i3−i3000000000000
χ352222-2-2-122-2-211-1-111-1-2-222-1-11100001-11-133−3−3−3−3332-2003−3−33-11-11000000000000
χ362222-2-2-122-2-211-1-111-1-2-222-1-11100001-11-133−3−3−3−333-2200−333−31-11-1000000000000
χ372222-2-2-122-2-211-1-111-1-2-222-1-11100001-11-1−3−33333−3−32-200−333−3-11-11000000000000
χ382222-2-2-122-2-211-1-111-1-2-222-1-11100001-11-1−3−33333−3−3-22003−3−331-11-1000000000000
χ392-2-222-222-22-222-2-2-2-2200002-22-2002i−2i000000002i−2i2i−2i0000000000002−22−2−i2i2−i2i20000
χ402-2-222-222-22-222-2-2-2-2200002-22-2002i−2i000000002i−2i2i−2i000000000000−22−22i2−i2i2−i20000
χ412-2-222-222-22-222-2-2-2-2200002-22-200−2i2i00000000−2i2i−2i2i0000000000002−22−2i2−i2i2−i20000
χ422-2-222-222-22-222-2-2-2-2200002-22-200−2i2i00000000−2i2i−2i2i000000000000−22−22−i2i2−i2i20000
χ432-2-222-22-22-2222-2-2-2-220000-22-222i−2i0000002i−2i2i−2i00000000000000002−2−22−i2i2i2−i20000
χ442-2-222-22-22-2222-2-2-2-220000-22-222i−2i0000002i−2i2i−2i0000000000000000−222−2i2−i2−i2i20000
χ452-2-222-22-22-2222-2-2-2-220000-22-22−2i2i000000−2i2i−2i2i00000000000000002−2−22i2−i2−i2i20000
χ462-2-222-22-22-2222-2-2-2-220000-22-22−2i2i000000−2i2i−2i2i0000000000000000−222−2−i2i2i2−i20000
χ47444444-2-4-4-4-4-2-2-2-2-2-2-24-44-422220000-2-22200000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-2-2-2-2-2-44-442222000022-2-200000000000000000000000000000000
χ494444-4-4-2-4-44422-2-222-24-4-4422-2-20000-222-200000000000000000000000000000000
χ504444-4-4-2-4-44422-2-222-2-444-422-2-200002-2-2200000000000000000000000000000000
χ514-4-444-4-24-44-4-2-22222-20000-22-22004i−4i00000000−2i2i−2i2i000000000000000000000000
χ524-4-444-4-24-44-4-2-22222-20000-22-2200−4i4i000000002i−2i2i−2i000000000000000000000000
χ534-4-444-4-2-44-44-2-22222-200002-22-24i−4i000000−2i2i−2i2i0000000000000000000000000000
χ544-4-444-4-2-44-44-2-22222-200002-22-2−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ554-4-44-4444-4-44-4-4-4-444400004-4-440000000000000000000000000000000000000000
χ564-4-44-444-444-4-4-4-4-44440000-444-40000000000000000000000000000000000000000
χ574-4-44-44-24-4-442222-2-2-20000-222-2000000000000−2i32i32i3−2i3000000000000000000000000
χ584-4-44-44-24-4-442222-2-2-20000-222-20000000000002i3−2i3−2i32i3000000000000000000000000
χ594-4-44-44-2-444-42222-2-2-200002-2-2200000000−2i32i32i3−2i30000000000000000000000000000
χ604-4-44-44-2-444-42222-2-2-200002-2-22000000002i3−2i3−2i32i30000000000000000000000000000
χ6188-8-80080000008-800-8000000000000000000000000000000000000000000000000
χ6288-8-800-40000−4i34i3-44−4i34i34000000000000000000000000000000000000000000000000
χ6388-8-800-400004i3−4i3-444i3−4i34000000000000000000000000000000000000000000000000
χ648-88-8008000000-8800-8000000000000000000000000000000000000000000000000
χ658-88-800-40000−4i34i34-44i3−4i34000000000000000000000000000000000000000000000000
χ668-88-800-400004i3−4i34-4−4i34i34000000000000000000000000000000000000000000000000

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