Finite Group Databasebeta

← Group #10691144

Character table — Group #10691144

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222234444446664446612121212121212124444888812122424242424242424444444448812121212242424244444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1
χ91111-1-111-1-1-1-1111111-1-1-1111-1-1-1-11ii−i−iii−i−i1-1iiii−i−i−i−i11-1-1ii−i−i1-1ii−i−i11-1-11-1i−iii−i−i1-1
χ101111-1-111-1-1-1-1111111-1-1-1111-1-1-1-11ii−i−iii−i−i1-1iiii−i−i−i−i-1-111−i−iii1-1ii−i−i11-1-1-11−ii−i−iii-11
χ111111-1-111-1-1-1-1111111-1-1-1111-1-1-1-11ii−i−i−i−iii1-1−i−i−i−iiiii11-1-1ii−i−i-11ii−i−i-1-1111-1i−i−i−iii-11
χ121111-1-111-1-1-1-1111111-1-1-1111-1-1-1-11ii−i−i−i−iii1-1−i−i−i−iiiii-1-111−i−iii-11ii−i−i-1-111-11−iiii−i−i1-1
χ131111-1-111-1-1-1-1111111-1-1-1111-1-1-1-11−i−iiiii−i−i1-1iiii−i−i−i−i11-1-1−i−iii-11−i−iii-1-1111-1−iiii−i−i-11
χ141111-1-111-1-1-1-1111111-1-1-1111-1-1-1-11−i−iiiii−i−i1-1iiii−i−i−i−i-1-111ii−i−i-11−i−iii-1-111-11i−i−i−iii1-1
χ151111-1-111-1-1-1-1111111-1-1-1111-1-1-1-11−i−iii−i−iii1-1−i−i−i−iiiii11-1-1−i−iii1-1−i−iii11-1-11-1−ii−i−iii1-1
χ161111-1-111-1-1-1-1111111-1-1-1111-1-1-1-11−i−iii−i−iii1-1−i−i−i−iiiii-1-111ii−i−i1-1−i−iii11-1-1-11i−iii−i−i-11
χ172222222222-2-22222-2-2-2222-2-222-2-2200000000-2-200000000222200000000000000-2-200000000
χ182222222222-2-22222-2-2-2222-2-222-2-2200000000-2-200000000-2-2-2-2000000000000002200000000
χ192222222-2-2-222-22222-2-222-2-2-2-2-222-2000000002-20000000000002222000000000000-2-2000000
χ202222222-2-2-222-22222-2-222-2-2-2-2-222-2000000002-2000000000000-2-2-2-200000000000022000000
χ212222222-2-2-2-2-2-2222-22222-222-2-2-2-2-22-22-20000-220000000000000000002-22-200000000000000
χ222222222-2-2-2-2-2-2222-22222-222-2-2-2-2-2-22-220000-22000000000000000000-22-2200000000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-2-1-1-1-111110000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100000000221111-1-1-1-10000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-222-1-11-1-1111112-22-200001-133−3−333−3−30000000000-11-113−33−30000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-222-1-11-1-1111112-22-200001-1−3−333−3−3330000000000-11-11−33−330000000000
χ29222222-1-2-2-2-2-2-2-1-1-1-222-1-11-1-111111-22-2200001-133−3−333−3−300000000001-11-1−33−330000000000
χ30222222-1-2-2-2-2-2-2-1-1-1-222-1-11-1-111111-22-2200001-1−3−333−3−33300000000001-11-13−33−30000000000
χ312222-2-222-2-2222222-2-22-2-22-2-2-2-222200000000-220000000022-2-200000000000000-2200000000
χ322222-2-222-2-2222222-2-22-2-22-2-2-2-222200000000-2200000000-2-222000000000000002-200000000
χ332222-2-22-22222-2222-22-2-2-2-2222222-22i−2i−2i2i0000-2-20000000000000000002i−2i−2i2i00000000000000
χ342222-2-22-22222-2222-22-2-2-2-2222222-2−2i2i2i−2i0000-2-2000000000000000000−2i2i2i−2i00000000000000
χ352222-2-22-222-2-2-22222-22-2-2-2-2-222-2-2-200000000220000000000002i2i−2i−2i000000000000−2i2i000000
χ362222-2-22-222-2-2-22222-22-2-2-2-2-222-2-2-20000000022000000000000−2i−2i2i2i0000000000002i−2i000000
χ372222-2-2-12-2-2-2-22-1-1-122-211-1-1-11111-12i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii000000002-2−i−iii-1-1110000000000
χ382222-2-2-12-2-2-2-22-1-1-122-211-1-1-11111-12i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i00000000-22−i−iii11-1-10000000000
χ392222-2-2-12-2-2-2-22-1-1-122-211-1-1-11111-1−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii00000000-22ii−i−i11-1-10000000000
χ402222-2-2-12-2-2-2-22-1-1-122-211-1-1-11111-1−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i000000002-2ii−i−i-1-1110000000000
χ412222-2-2-1-22222-2-1-1-1-22-2111-1-1-1-1-1-112i−2i−2i2i000011−i3−i3i3i3i3i3−i3−i30000000000−iii−i−333−30000000000
χ422222-2-2-1-22222-2-1-1-1-22-2111-1-1-1-1-1-112i−2i−2i2i000011i3i3−i3−i3−i3−i3i3i30000000000−iii−i3−3−330000000000
χ432222-2-2-1-22222-2-1-1-1-22-2111-1-1-1-1-1-11−2i2i2i−2i000011−i3−i3i3i3i3i3−i3−i30000000000i−i−ii3−3−330000000000
χ442222-2-2-1-22222-2-1-1-1-22-2111-1-1-1-1-1-11−2i2i2i−2i000011i3i3−i3−i3−i3−i3i3i30000000000i−i−ii−333−30000000000
χ452-2-222-2222-200-22-2-2000-222002-200-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000000000002−22−200
χ462-2-222-2222-200-22-2-2000-222002-200-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i000000000000000000−22−2200
χ472-2-222-2222-200-22-2-2000-222002-200-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i000000000000000000−22−2200
χ482-2-222-2222-200-22-2-2000-222002-200-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000000000002−22−200
χ492-2-22-2222-2200-22-2-20002-2200-2200-200002−2−22002−22−2−22−222i−2i−2i2i000000000000000000i2−i2−i2i200
χ502-2-22-2222-2200-22-2-20002-2200-2200-200002−2−22002−22−2−22−22−2i2i2i−2i000000000000000000−i2i2i2−i200
χ512-2-22-2222-2200-22-2-20002-2200-2200-20000−222−200−22−222−22−22i−2i−2i2i000000000000000000−i2i2i2−i200
χ522-2-22-2222-2200-22-2-20002-2200-2200-20000−222−200−22−222−22−2−2i2i2i−2i000000000000000000i2−i2−i2i200
χ53444444-2444-4-44-2-2-2-4-4-4-2-2-222-2-222-20000000022000000000000000000000000000000000000
χ54444444-2-4-4-444-4-2-2-24-4-4-2-222222-2-2200000000-22000000000000000000000000000000000000
χ554444-4-4-24-4-4444-2-2-2-4-4422-22222-2-2-2000000002-2000000000000000000000000000000000000
χ564444-4-4-2-444-4-4-4-2-2-24-4422222-2-222200000000-2-2000000000000000000000000000000000000
χ574-44-40040004i−4i0-44-400000000004i−4i000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ584-44-40040004i−4i0-44-400000000004i−4i00000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ594-44-4004000−4i4i0-44-40000000000−4i4i000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ604-44-4004000−4i4i0-44-40000000000−4i4i00000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ614-4-444-44-4-440044-4-4000-44-400-440040000000000000000000000000000000000000000000000
χ624-4-444-4-244-400-4-2220002-2-200-220020000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ634-4-444-4-244-400-4-2220002-2-200-2200200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ644-4-444-4-2-4-44004-2220002-22002-200-20000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ654-4-444-4-2-4-44004-2220002-22002-200-20000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ664-4-44-444-44-40044-4-40004-4-4004-40040000000000000000000000000000000000000000000000
χ674-4-44-44-24-4400-4-222000-22-2002-2002000022−22−222200−22−222−22−20000000000000000000000000000
χ684-4-44-44-24-4400-4-222000-22-2002-20020000−222222−22002−22−2−22−220000000000000000000000000000
χ694-4-44-44-2-44-4004-222000-22200-2200-200000000006−6−66−666−60000000000000000000000000000
χ704-4-44-44-2-44-4004-222000-22200-2200-20000000000−666−66−6−660000000000000000000000000000
χ7188-8-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ7288-8-800-400000044-400000043−43000000000000000000000000000000000000000000000000000
χ7388-8-800-400000044-4000000−4343000000000000000000000000000000000000000000000000000
χ748-88-800-40008i−8i04-440000000000−4i4i00000000000000000000000000000000000000000000000
χ758-88-800-4000−8i8i04-4400000000004i−4i00000000000000000000000000000000000000000000000

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