Finite Group Databasebeta

← Group #10692468

Character table — Group #10692468

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order12222234466644444661212121212121212444488881212121212121212121288888824242424242424242444882288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1
χ91111-1-11-1-111111-11-1-1-111-1-111-1-1ii−i−ii−ii−i1-1iiii−i−i−i−iii−i−i1-1ii−i−i11-1-111-1-1i−i1-1i−i
χ101111-1-11-1-111111-11-1-1-111-1-111-1-1ii−i−ii−ii−i1-1iiii−i−i−i−i−i−iii1-1ii−i−i11-1-1-1-111−ii-11−ii
χ111111-1-11-1-111111-11-1-1-111-1-111-1-1ii−i−i−ii−ii1-1iiii−i−i−i−iii−i−i-11−i−iii-1-111-1-111i−i1-1−ii
χ121111-1-11-1-111111-11-1-1-111-1-111-1-1ii−i−i−ii−ii1-1iiii−i−i−i−i−i−iii-11−i−iii-1-11111-1-1−ii-11i−i
χ131111-1-11-1-111111-11-1-1-111-1-111-1-1−i−iiii−ii−i1-1−i−i−i−iiiiiii−i−i-11ii−i−i-1-11111-1-1i−i-11−ii
χ141111-1-11-1-111111-11-1-1-111-1-111-1-1−i−iiii−ii−i1-1−i−i−i−iiiii−i−iii-11ii−i−i-1-111-1-111−ii1-1i−i
χ151111-1-11-1-111111-11-1-1-111-1-111-1-1−i−iii−ii−ii1-1−i−i−i−iiiiiii−i−i1-1−i−iii11-1-1-1-111i−i-11i−i
χ161111-1-11-1-111111-11-1-1-111-1-111-1-1−i−iii−ii−ii1-1−i−i−i−iiiii−i−iii1-1−i−iii11-1-111-1-1−ii1-1−ii
χ172222222222222-2-2-2-222-2-2-2-2-2-222000000002-200000000222200000000000000-2-20000
χ182222222222222-2-2-2-222-2-2-2-2-2-222000000002-200000000-2-2-2-200000000000000220000
χ192222222-2-2222-222-2-2222222-2-2-2-200002i−2i−2i2i-2-2000000000000002i−2i2i−2i00000000000000
χ202222222-2-2222-222-2-2222222-2-2-2-20000−2i2i2i−2i-2-200000000000000−2i2i−2i2i00000000000000
χ212222222-2-2222-2-2-22222-2-2-2-222-2-200000000-2200000000000000000000002-22-2000000
χ222222222-2-2222-2-2-22222-2-2-2-222-2-200000000-220000000000000000000000-22-22000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-10000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2111111110000000000
χ25222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1111111110000-2-2-1-1-1-111110000000000
χ26222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-10000000000
χ27222222-1-2-2-1-1-1-222-2-2-1-1-1-1-1-1111100002i−2i−2i2i11−i3−i3i3i3−i3−i3i3i3000000−ii−ii3−33−30000000000
χ28222222-1-2-2-1-1-1-222-2-2-1-1-1-1-1-1111100002i−2i−2i2i11i3i3−i3−i3i3i3−i3−i3000000−ii−ii−33−330000000000
χ29222222-1-2-2-1-1-1-222-2-2-1-1-1-1-1-111110000−2i2i2i−2i11−i3−i3i3i3−i3−i3i3i3000000i−ii−i−33−330000000000
χ30222222-1-2-2-1-1-1-222-2-2-1-1-1-1-1-111110000−2i2i2i−2i11i3i3−i3−i3i3i3−i3−i3000000i−ii−i3−33−30000000000
χ312222-2-2222222-22-2-22-2-222-2-2-2-222000022-2-2-22000000000000002-2-2200000000000000
χ322222-2-2222222-22-2-22-2-222-2-2-2-2220000-2-222-2200000000000000-222-200000000000000
χ332222-2-2222222-2-222-2-2-2-2-222222200000000-2-200000000000000000000002-2-22000000
χ342222-2-2222222-2-222-2-2-2-2-222222200000000-2-20000000000000000000000-222-2000000
χ352222-2-22-2-22222-22-22-2-2-2-222-2-2-2-20000000022000000002i2i−2i−2i00000000000000−2i2i0000
χ362222-2-22-2-22222-22-22-2-2-2-222-2-2-2-2000000002200000000−2i−2i2i2i000000000000002i−2i0000
χ372222-2-2-122-1-1-1-22-2-2211-1-11111-1-1000022-2-21-133−3−3−3−333000000-111-1−333−30000000000
χ382222-2-2-122-1-1-1-22-2-2211-1-11111-1-1000022-2-21-1−3−33333−3−3000000-111-13−3−330000000000
χ392222-2-2-122-1-1-1-22-2-2211-1-11111-1-10000-2-2221-133−3−3−3−3330000001-1-113−3−330000000000
χ402222-2-2-122-1-1-1-22-2-2211-1-11111-1-10000-2-2221-1−3−33333−3−30000001-1-11−333−30000000000
χ412222-2-2-1-2-2-1-1-122-22-211-1-111-1-1112i2i−2i−2i2i−2i2i−2i-11−i−i−i−iiiii00002-2−i−iii-1-1110000000000
χ422222-2-2-1-2-2-1-1-122-22-211-1-111-1-1112i2i−2i−2i−2i2i−2i2i-11−i−i−i−iiiii0000-22ii−i−i11-1-10000000000
χ432222-2-2-1-2-2-1-1-122-22-211-1-111-1-111−2i−2i2i2i2i−2i2i−2i-11iiii−i−i−i−i0000-22−i−iii11-1-10000000000
χ442222-2-2-1-2-2-1-1-122-22-211-1-111-1-111−2i−2i2i2i−2i2i−2i2i-11iiii−i−i−i−i00002-2ii−i−i-1-1110000000000
χ45444444-244-2-2-24-4-4-4-4-2-2222222-2-200000000-2200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-4-4-444-2-22222-2-222000000002-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-4-444-42222-2-2-2-2-2-2000000002200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-24-44-442222-2-2222200000000-2-200000000000000000000000000000000
χ4944-4-40044-44-4-400000000000004-42i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5044-4-40044-44-4-400000000000004-4−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5144-4-4004-444-4-40000000000000-442-2-220000002-22-2-22-22000000000000000000000000
χ5244-4-4004-444-4-40000000000000-44-222-2000000-22-222-22-2000000000000000000000000
χ5344-4-400-24-4-22200000000023−2323−23-222i−2i2i−2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ5444-4-400-24-4-22200000000023−2323−23-22−2i2i−2i2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ5544-4-400-24-4-222000000000−2323−2323-222i−2i2i−2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ5644-4-400-24-4-222000000000−2323−2323-22−2i2i−2i2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ5744-4-400-2-44-22200000000023−23−23232-22-2-22000000−1+31−3−1−31+31+3−1−31−3−1+3000000000000000000000000
χ5844-4-400-2-44-22200000000023−23−23232-2-222-20000001−3−1+31+3−1−3−1−31+3−1+31−3000000000000000000000000
χ5944-4-400-2-44-222000000000−232323−232-22-2-22000000−1−31+3−1+31−31−3−1+31+3−1−3000000000000000000000000
χ6044-4-400-2-44-222000000000−232323−232-2-222-20000001+3−1−31−3−1+3−1+31−3−1−31+3000000000000000000000000
χ614-44-44-4400-44-4000004-400000000000000000000000000−2i22i2−2i22i200000000000000000000
χ624-44-44-4400-44-4000004-4000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ634-44-4-44400-44-400000-440000000000000000000000000022−22−222200000000000000000000
χ644-44-4-44400-44-400000-4400000000000000000000000000−222222−2200000000000000000000
χ658-88-88-8-4004-4400000-4400000000000000000000000000000000000000000000000000
χ668-88-8-88-4004-44000004-400000000000000000000000000000000000000000000000000
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-4000000043−43000000000000000000000000000000000000000000000000
χ698-8-8800-40044-40000000−4343000000000000000000000000000000000000000000000000

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