Finite Group Databasebeta

← Group #10691502

Character table — Group #10691502

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order122222344444466622466121212121212121266888888882424242424242424444488888824242424242424244444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ411111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111
χ9111111111-1-1-1-1111-1-11111111-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-111-1-1ii−i−ii−iii−i−iii−i−i1-1ii−i−ii−i1-1
χ10111111111-1-1-1-1111-1-11111111-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-1-1-111−i−iiii−iii−i−iii−i−i-11−i−iii−ii-11
χ11111111111-1-1-1-1111-1-11111111-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-111-1-1−i−iii−ii−i−iii−i−iii1-1−i−iii−ii1-1
χ12111111111-1-1-1-1111-1-11111111-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-1-1-111ii−i−i−ii−i−iii−i−iii-11ii−i−ii−i-11
χ13111111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111ii−i−i-1-1-1-1111111-1-1ii−i−i−iiii−i−i−i−iii1-1−i−iiii−i-11
χ14111111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111ii−i−i-1-1-1-11111-1-111−i−iii−iiii−i−i−i−iii-11ii−i−i−ii1-1
χ15111111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111−i−iii-1-1-1-1111111-1-1−i−iiii−i−i−iiiii−i−i1-1ii−i−i−ii-11
χ16111111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111−i−iii-1-1-1-11111-1-111ii−i−ii−i−i−iiiii−i−i-11−i−iiii−i1-1
χ172222222-2-22222222-2-2-222-2-2-2-22222-2-20000000000000000000022220000000000000000-2-200
χ182222222-2-22222222-2-2-222-2-2-2-22222-2-200000000000000000000-2-2-2-200000000000000002200
χ192222222-2-2-2-2-2-222222-222-2-2-2-2-2-2-2-222000000000000000000002i2i−2i−2i0000000000000000−2i2i00
χ202222222-2-2-2-2-2-222222-222-2-2-2-2-2-2-2-22200000000000000000000−2i−2i2i2i00000000000000002i−2i00
χ21222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111100000000-2-2-1-1-1-111110000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111100000000221111-1-1-1-10000000000
χ25222222-122-2-2-2-2-1-1-1-2-22-1-1-1-1-1-111111122-2-22i2i−2i−2i-1-1-1-11111000000002i−2i−i−iii−i−iii0000000000
χ26222222-122-2-2-2-2-1-1-1-2-22-1-1-1-1-1-111111122-2-2−2i−2i2i2i-1-1-1-1111100000000−2i2iii−i−iii−i−i0000000000
χ27222222-122-2-2-2-2-1-1-1-2-22-1-1-1-1-1-1111111-2-2222i2i−2i−2i1111-1-1-1-100000000−2i2i−i−iiiii−i−i0000000000
χ28222222-122-2-2-2-2-1-1-1-2-22-1-1-1-1-1-1111111-2-222−2i−2i2i2i1111-1-1-1-1000000002i−2iii−i−i−i−iii0000000000
χ292222-2-222222-2-2222-22-2-2-2-2-22222-2-22-2000000000000000022-2-200000000000000-2200000000
χ302222-2-222222-2-2222-22-2-2-2-2-22222-2-22-20000000000000000-2-222000000000000002-200000000
χ312222-2-2222-2-2222222-2-2-2-2-2-222-2-222-220000000000000000222200000000000000-2-200000000
χ322222-2-2222-2-2222222-2-2-2-2-2-222-2-222-220000000000000000-2-2-2-2000000000000002200000000
χ332222-2-22-2-222-2-22222-22-2-222-2-222-2-2-2200002i−2i2i−2i0000000000000000002i−2i2i−2i00000000000000
χ342222-2-22-2-222-2-22222-22-2-222-2-222-2-2-220000−2i2i−2i2i000000000000000000−2i2i−2i2i00000000000000
χ352222-2-22-2-2-2-222222-222-2-222-2-2-2-2222-200002-2-220000000000000000002-2-2200000000000000
χ362222-2-22-2-2-2-222222-222-2-222-2-2-2-2222-20000-222-2000000000000000000-222-200000000000000
χ372222-2-2-1-2-222-2-2-1-1-12-2211-1-111-1-1111-100002i−2i2i−2i33−3−333−3−30000000000−ii−ii−i3i3−i3i30000000000
χ382222-2-2-1-2-222-2-2-1-1-12-2211-1-111-1-1111-100002i−2i2i−2i−3−333−3−3330000000000−ii−iii3−i3i3−i30000000000
χ392222-2-2-1-2-222-2-2-1-1-12-2211-1-111-1-1111-10000−2i2i−2i2i33−3−333−3−30000000000i−ii−ii3−i3i3−i30000000000
χ402222-2-2-1-2-222-2-2-1-1-12-2211-1-111-1-1111-10000−2i2i−2i2i−3−333−3−3330000000000i−ii−i−i3i3−i3i30000000000
χ412222-2-2-1-2-2-2-222-1-1-1-22211-1-11111-1-1-1100002-2-2233−3−3−3−3330000000000-111-1−333−30000000000
χ422222-2-2-1-2-2-2-222-1-1-1-22211-1-11111-1-1-1100002-2-22−3−33333−3−30000000000-111-13−3−330000000000
χ432222-2-2-1-2-2-2-222-1-1-1-22211-1-11111-1-1-110000-222-233−3−3−3−33300000000001-1-113−3−330000000000
χ442222-2-2-1-2-2-2-222-1-1-1-22211-1-11111-1-1-110000-222-2−3−33333−3−300000000001-1-11−333−30000000000
χ452-2-222-22002i−2i2i−2i2-2-20002-200002i−2i2i−2i002−2−i2i200002−22−2−i2i2−i2i20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000001−i−1+i1+i−1−i0000
χ462-2-222-22002i−2i2i−2i2-2-20002-200002i−2i2i−2i002−2−i2i200002−22−2−i2i2−i2i200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−1+i1−i−1−i1+i0000
χ472-2-222-22002i−2i2i−2i2-2-20002-200002i−2i2i−2i00−22i2−i20000−22−22i2−i2i2−i20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−1+i1−i−1−i1+i0000
χ482-2-222-22002i−2i2i−2i2-2-20002-200002i−2i2i−2i00−22i2−i20000−22−22i2−i2i2−i200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000001−i−1+i1+i−1−i0000
χ492-2-222-2200−2i2i−2i2i2-2-20002-20000−2i2i−2i2i002−2i2−i200002−22−2i2−i2i2−i200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000001+i−1−i1−i−1+i0000
χ502-2-222-2200−2i2i−2i2i2-2-20002-20000−2i2i−2i2i002−2i2−i200002−22−2i2−i2i2−i20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−1−i1+i−1+i1−i0000
χ512-2-222-2200−2i2i−2i2i2-2-20002-20000−2i2i−2i2i00−22−i2i20000−22−22−i2i2−i2i200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−1−i1+i−1+i1−i0000
χ522-2-222-2200−2i2i−2i2i2-2-20002-20000−2i2i−2i2i00−22−i2i20000−22−22−i2i2−i2i20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000001+i−1−i1−i−1+i0000
χ53444444-2-4-44444-2-2-2-4-4-4-2-22222-2-2-2-22200000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-244-4-2-222222222-2-200000000000000000000000000000000000000000000
χ554444-4-4-24444-4-4-2-2-2-44-42222-2-2-2-222-2200000000000000000000000000000000000000000000
χ564444-4-4-244-4-444-2-2-24-4-42222-2-222-2-22-200000000000000000000000000000000000000000000
χ574-44-40044-40000-4-4400000004-40000000000000000000000004i−4i000000000000000000000000
χ584-44-40044-40000-4-4400000004-4000000000000000000000000−4i4i000000000000000000000000
χ594-44-4004-440000-4-440000000-4400000000000000000000004i−4i00000000000000000000000000
χ604-44-4004-440000-4-440000000-440000000000000000000000−4i4i00000000000000000000000000
χ614-4-444-4-2004i−4i4i−4i-222000-220000−2i2i−2i2i0022−22−2i22i20000−22−22i2−i2i2−i20000000000000000000000000000
χ624-4-444-4-2004i−4i4i−4i-222000-220000−2i2i−2i2i00−22222i2−2i200002−22−2−i2i2−i2i20000000000000000000000000000
χ634-4-444-4-200−4i4i−4i4i-222000-2200002i−2i2i−2i0022−222i2−2i20000−22−22−i2i2−i2i20000000000000000000000000000
χ644-4-444-4-200−4i4i−4i4i-222000-2200002i−2i2i−2i00−2222−2i22i200002−22−2i2−i2i2−i20000000000000000000000000000
χ654-4-44-444004i−4i−4i4i4-4-4000-4400004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-4-44-44400−4i4i4i−4i4-4-4000-440000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-4-44-44-2004i−4i−4i4i-2220002-20000−2i2i2i−2i00000000006−6−66−i6i6i6−i60000000000000000000000000000
χ684-4-44-44-2004i−4i−4i4i-2220002-20000−2i2i2i−2i0000000000−666−6i6−i6−i6i60000000000000000000000000000
χ694-4-44-44-200−4i4i4i−4i-2220002-200002i−2i−2i2i00000000006−6−66i6−i6−i6i60000000000000000000000000000
χ704-4-44-44-200−4i4i4i−4i-2220002-200002i−2i−2i2i0000000000−666−6−i6i6i6−i60000000000000000000000000000
χ7188-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000
χ7288-8-800-40000004-440000043−430000000000000000000000000000000000000000000000000000
χ7388-8-800-40000004-4400000−43430000000000000000000000000000000000000000000000000000
χ748-88-800-48-8000044-40000000-4400000000000000000000000000000000000000000000000000
χ758-88-800-4-88000044-400000004-400000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.