Finite Group Databasebeta

← Group #10691032

Character table — Group #10691032

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222234444446664446612121212121212124444888812121212121212121212444488888824242424242424244488888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ511111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
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
χ91111-1-11-1-111-1-111111-1-1-111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-1ii−i−i1-1ii−i−i11-1-1-11i−iii−i−i1-1
χ101111-1-11-1-111-1-111111-1-1-111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i-1-111−i−iii1-1ii−i−i11-1-11-1−ii−i−iii-11
χ111111-1-11-1-111-1-111111-1-1-111-1-111-1-1ii−i−i−i−iii1-1iiii−i−i−i−i11-1-1−i−iii-11−i−iii-1-111-11−iiii−i−i-11
χ121111-1-11-1-111-1-111111-1-1-111-1-111-1-1ii−i−i−i−iii1-1iiii−i−i−i−i-1-111ii−i−i-11−i−iii-1-1111-1i−i−i−iii1-1
χ131111-1-11-1-111-1-111111-1-1-111-1-111-1-1−i−iiiii−i−i1-1−i−i−i−iiiii11-1-1ii−i−i-11ii−i−i-1-111-11i−i−i−iii-11
χ141111-1-11-1-111-1-111111-1-1-111-1-111-1-1−i−iiiii−i−i1-1−i−i−i−iiiii-1-111−i−iii-11ii−i−i-1-1111-1−iiii−i−i1-1
χ151111-1-11-1-111-1-111111-1-1-111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-1−i−iii1-1−i−iii11-1-1-11−ii−i−iii1-1
χ161111-1-11-1-111-1-111111-1-1-111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii-1-111ii−i−i1-1−i−iii11-1-11-1i−iii−i−i-11
χ17222222222-2-2-2-22222-2-2222222-2-2-2-200002i−2i2i−2i-2-20000000000000000002i−2i2i−2i00000000000000
χ18222222222-2-2-2-22222-2-2222222-2-2-2-20000−2i2i−2i2i-2-2000000000000000000−2i2i−2i2i00000000000000
χ192222222-2-222-2-2222-2-2222-2-2-2-222-2-200000000-220000000022-2-2000000000000002-200000000
χ202222222-2-222-2-2222-2-2222-2-2-2-222-2-200000000-2200000000-2-22200000000000000-2200000000
χ212222222-2-2-2-222222-22-222-2-2-2-2-2-222000000002-20000000000002222000000000000-2-2000000
χ222222222-2-2-2-222222-22-222-2-2-2-2-2-222000000002-2000000000000-2-2-2-200000000000022000000
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
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-11111111100000000-2-2-1-1-1-111110000000000
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
χ27222222-122-2-2-2-2-1-1-12-2-2-1-1-1-1-1-1111100002i−2i2i−2i11−i3−i3i3i3−i3−i3i3i30000000000−ii−ii3−33−30000000000
χ28222222-122-2-2-2-2-1-1-12-2-2-1-1-1-1-1-1111100002i−2i2i−2i11i3i3−i3−i3i3i3−i3−i30000000000−ii−ii−33−330000000000
χ29222222-122-2-2-2-2-1-1-12-2-2-1-1-1-1-1-111110000−2i2i−2i2i11−i3−i3i3i3−i3−i3i3i30000000000i−ii−i−33−330000000000
χ30222222-122-2-2-2-2-1-1-12-2-2-1-1-1-1-1-111110000−2i2i−2i2i11i3i3−i3−i3i3i3−i3−i30000000000i−ii−i3−33−30000000000
χ312222-2-22222222222-2-2-2-2-2-2-222222200000000-2-200000000222200000000000000-2-200000000
χ322222-2-22222222222-2-2-2-2-2-2-222222200000000-2-200000000-2-2-2-2000000000000002200000000
χ332222-2-2222-2-2-2-2222-222-2-2-2-222-2-2-2-200000000220000000000002i2i−2i−2i000000000000−2i2i000000
χ342222-2-2222-2-2-2-2222-222-2-2-2-222-2-2-2-20000000022000000000000−2i−2i2i2i0000000000002i−2i000000
χ352222-2-22-2-2-2-2222222-22-2-222-2-2-2-22200002-2-22-220000000000000000002-2-2200000000000000
χ362222-2-22-2-2-2-2222222-22-2-222-2-2-2-2220000-222-2-22000000000000000000-222-200000000000000
χ372222-2-2-1-2-222-2-2-1-1-122-211-1-111-1-1112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii000000002-2−i−iii-1-1110000000000
χ382222-2-2-1-2-222-2-2-1-1-122-211-1-111-1-1112i2i−2i−2i−2i−2i2i2i-11−i−i−i−iiiii00000000-22ii−i−i11-1-10000000000
χ392222-2-2-1-2-222-2-2-1-1-122-211-1-111-1-111−2i−2i2i2i2i2i−2i−2i-11iiii−i−i−i−i00000000-22−i−iii11-1-10000000000
χ402222-2-2-1-2-222-2-2-1-1-122-211-1-111-1-111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i000000002-2ii−i−i-1-1110000000000
χ412222-2-2-1-2-2-2-222-1-1-12-2211-1-11111-1-100002-2-221-133−3−3−3−3330000000000-111-1−333−30000000000
χ422222-2-2-1-2-2-2-222-1-1-12-2211-1-11111-1-100002-2-221-1−3−33333−3−30000000000-111-13−3−330000000000
χ432222-2-2-1-2-2-2-222-1-1-12-2211-1-11111-1-10000-222-21-133−3−3−3−33300000000001-1-113−3−330000000000
χ442222-2-2-1-2-2-2-222-1-1-12-2211-1-11111-1-10000-222-21-1−3−33333−3−300000000001-1-11−333−30000000000
χ452-2-220022i−2i2-22i−2i2-2-200000002i−2i2-22i−2i1+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2-20000000000000000001−i−1+i1+i−1−i00
χ462-2-220022i−2i2-22i−2i2-2-200000002i−2i2-22i−2i1+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i-22000000000000000000−1+i1−i−1−i1+i00
χ472-2-220022i−2i2-22i−2i2-2-200000002i−2i2-22i−2i−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2-2000000000000000000−1+i1−i−1−i1+i00
χ482-2-220022i−2i2-22i−2i2-2-200000002i−2i2-22i−2i−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i-220000000000000000001−i−1+i1+i−1−i00
χ492-2-22002−2i2i2-2−2i2i2-2-20000000−2i2i2-2−2i2i1−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i-22000000000000000000−1−i1+i−1+i1−i00
χ502-2-22002−2i2i2-2−2i2i2-2-20000000−2i2i2-2−2i2i1−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i2-20000000000000000001+i−1−i1−i−1+i00
χ512-2-22002−2i2i2-2−2i2i2-2-20000000−2i2i2-2−2i2i−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i-220000000000000000001+i−1−i1−i−1+i00
χ522-2-22002−2i2i2-2−2i2i2-2-20000000−2i2i2-2−2i2i−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i2-2000000000000000000−1−i1+i−1+i1−i00
χ53444444-2-4-444-4-4-2-2-2-4-44-2-22222-2-222000000002-2000000000000000000000000000000000000
χ54444444-2-4-4-4-444-2-2-2-44-4-2-2222222-2-200000000-22000000000000000000000000000000000000
χ554444-4-4-2444444-2-2-2-4-4-42222-2-2-2-2-2-20000000022000000000000000000000000000000000000
χ564444-4-4-244-4-4-4-4-2-2-2-4442222-2-2222200000000-2-2000000000000000000000000000000000000
χ5744-4-44-44000000-44-40004-400000000000000000000000000000022−2222−2200000000000000000000
χ5844-4-44-44000000-44-40004-4000000000000000000000000000000−2222−222200000000000000000000
χ5944-4-4-444000000-44-4000-44000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ6044-4-4-444000000-44-4000-440000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ614-4-440044i−4i-44−4i4i4-4-400000004i−4i-44−4i4i0000000000000000000000000000000000000000000000
χ624-4-44004−4i4i-444i−4i4-4-40000000−4i4i-444i−4i0000000000000000000000000000000000000000000000
χ634-4-4400-24i−4i4-44i−4i-2220000000−2i2i-22−2i2i2+2i−2−2i2−2i−2+2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000
χ644-4-4400-24i−4i4-44i−4i-2220000000−2i2i-22−2i2i−2−2i2+2i−2+2i2−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000
χ654-4-4400-24i−4i-44−4i4i-2220000000−2i2i2-22i−2i0000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000
χ664-4-4400-24i−4i-44−4i4i-2220000000−2i2i2-22i−2i0000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ674-4-4400-2−4i4i4-4−4i4i-22200000002i−2i-222i−2i2−2i−2+2i2+2i−2−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000
χ684-4-4400-2−4i4i4-4−4i4i-22200000002i−2i-222i−2i−2+2i2−2i−2−2i2+2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000
χ694-4-4400-2−4i4i-444i−4i-22200000002i−2i2-2−2i2i0000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000
χ704-4-4400-2−4i4i-444i−4i-22200000002i−2i2-2−2i2i0000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ7188-8-88-8-40000004-44000-44000000000000000000000000000000000000000000000000000000
χ7288-8-8-88-40000004-440004-4000000000000000000000000000000000000000000000000000000
χ738-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-88-800-400000044-40000043−430000000000000000000000000000000000000000000000000000
χ758-88-800-400000044-400000−43430000000000000000000000000000000000000000000000000000

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