Finite Group Databasebeta

← Group #10692403

Character table — Group #10692403

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order12223444466624444668888121212121212121288121224242424242424244488121212122424242424448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ911111-1-1-1-1111-111-11-1-1ii−i−i11-1-111-1-1i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-1
χ1011111-1-1-1-1111-111-11-1-1ii−i−i11-1-111-1-1i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-1-1-111−i−iii−i−iii-11
χ1111111-1-1-1-1111-111-11-1-1ii−i−i11-1-111-1-1i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-11111-1-1−i−iiiii−i−i-11
χ1211111-1-1-1-1111-111-11-1-1ii−i−i11-1-111-1-1i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-111-1-111ii−i−i−i−iii1-1
χ1311111-1-1-1-1111-111-11-1-1−i−iii11-1-111-1-1−ii1-1−i−i−i−iiiiii−i-11ii−i−i-1-11111-1-1ii−i−i−i−iii-11
χ1411111-1-1-1-1111-111-11-1-1−i−iii11-1-111-1-1−ii1-1−i−i−i−iiiiii−i-11ii−i−i-1-111-1-111−i−iiiii−i−i1-1
χ1511111-1-1-1-1111-111-11-1-1−i−iii11-1-111-1-1−ii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-111-1-1−i−iii−i−iii1-1
χ1611111-1-1-1-1111-111-11-1-1−i−iii11-1-111-1-1−ii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-1-1-111ii−i−iii−i−i-11
χ17222222222222-22-2-2-2-2-222222222-2-222-2-2-2-222-2-222-2-200000000000000000000000000
χ18222222222222-22-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222-2-22200000000000000000000000000
χ192222222-2-22222-2-2-22220000-2-22222-2-200-2-2000000000000000000002-22-20000000000
χ202222222-2-22222-2-2-22220000-2-22222-2-200-2-200000000000000000000-22-220000000000
χ212222222-2-2222-2-222-2-2-20000-2-222-2-2-2-2002200000000000000000000000000002i−2i2i−2i00
χ222222222-2-2222-2-222-2-2-20000-2-222-2-2-2-200220000000000000000000000000000−2i2i−2i2i00
χ2322222-2-2222222-22-2-2220000-2-2-2-2-2-222002-200000000000000000000000000002-2-2200
χ2422222-2-2222222-22-2-2220000-2-2-2-2-2-222002-20000000000000000000000000000-222-200
χ2522222-2-222222-2-2-222-2-20000-2-2-2-2222200-22000000000000000000002-2-220000000000
χ2622222-2-222222-2-2-222-2-20000-2-2-2-2222200-2200000000000000000000-222-20000000000
χ2722222-2-2-2-222222-22-2222i2i−2i−2i22-2-2-2-2-2-2−2i2i-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ2822222-2-2-2-222222-22-222−2i−2i2i2i22-2-2-2-2-2-22i−2i-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ292222-12222-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ302222-12222-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ312222-12222-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ322222-12222-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ332222-12222-1-1-1-22-2-2-2112222-1-1-1-111-1-1-2-211-1-111-1-11100003−33−33−33−300000000000000
χ342222-12222-1-1-1-22-2-2-2112222-1-1-1-111-1-1-2-211-1-111-1-1110000−33−33−33−3300000000000000
χ352222-12222-1-1-1-22-2-2-211-2-2-2-2-1-1-1-111-1-1221111-1-111-1-100003−33−3−33−3300000000000000
χ362222-12222-1-1-1-22-2-2-211-2-2-2-2-1-1-1-111-1-1221111-1-111-1-10000−33−333−33−300000000000000
χ372222-1-2-2-2-2-1-1-122-22-2-1-12i2i−2i−2i-1-1111111−2i2i1-1−i−iiiii−i−i0000−i3i3i3−i3−333−300000000000000
χ382222-1-2-2-2-2-1-1-122-22-2-1-12i2i−2i−2i-1-1111111−2i2i1-1−i−iiiii−i−i0000i3−i3−i3i33−3−3300000000000000
χ392222-1-2-2-2-2-1-1-122-22-2-1-1−2i−2i2i2i-1-11111112i−2i1-1ii−i−i−i−iii0000−i3i3i3−i33−3−3300000000000000
χ402222-1-2-2-2-2-1-1-122-22-2-1-1−2i−2i2i2i-1-11111112i−2i1-1ii−i−i−i−iii0000i3−i3−i3i3−333−300000000000000
χ412222-1-2-2-2-2-1-1-1-222-22112i2i−2i−2i-1-111-1-1112i−2i-11−i−i−i−iiiii2i−2i2-2−i−iii-1-11100000000000000
χ422222-1-2-2-2-2-1-1-1-222-22112i2i−2i−2i-1-111-1-1112i−2i-11−i−i−i−iiiii−2i2i-22ii−i−i11-1-100000000000000
χ432222-1-2-2-2-2-1-1-1-222-2211−2i−2i2i2i-1-111-1-111−2i2i-11iiii−i−i−i−i2i−2i-22−i−iii11-1-100000000000000
χ442222-1-2-2-2-2-1-1-1-222-2211−2i−2i2i2i-1-111-1-111−2i2i-11iiii−i−i−i−i−2i2i2-2ii−i−i-1-11100000000000000
χ454444-244-4-4-2-2-24-4-4-44-2-2000022-2-2-2-22200220000000000000000000000000000000000
χ464444-244-4-4-2-2-2-4-444-422000022-2-2222200-2-20000000000000000000000000000000000
χ474444-2-4-444-2-2-24-44-4-4-2-20000222222-2-200-220000000000000000000000000000000000
χ484444-2-4-444-2-2-2-4-4-4442200002222-2-2-2-2002-20000000000000000000000000000000000
χ494-44-44004i−4i4-4-4000000000000000004i−4i00000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ504-44-44004i−4i4-4-4000000000000000004i−4i0000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ514-44-4400−4i4i4-4-400000000000000000−4i4i0000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ524-44-4400−4i4i4-4-400000000000000000−4i4i00000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ534-4-4444i−4i00-44-400000002+2i−2−2i2−2i−2+2i004i−4i000000002+2i−2−2i002−2i−2+2i0000000000000000000000000000
χ544-4-4444i−4i00-44-40000000−2−2i2+2i−2+2i2−2i004i−4i00000000−2−2i2+2i00−2+2i2−2i0000000000000000000000000000
χ554-4-444−4i4i00-44-400000002−2i−2+2i2+2i−2−2i00−4i4i000000002−2i−2+2i002+2i−2−2i0000000000000000000000000000
χ564-4-444−4i4i00-44-40000000−2+2i2−2i−2−2i2+2i00−4i4i00000000−2+2i2−2i00−2−2i2+2i0000000000000000000000000000
χ574-4-44-24i−4i002-2200000−2i32i32+2i−2−2i2−2i−2+2i00−2i2i23−23000000−1−i1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−1+i1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000
χ584-4-44-24i−4i002-2200000−2i32i3−2−2i2+2i−2+2i2−2i00−2i2i23−230000001+i−1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ221−i−1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000
χ594-4-44-24i−4i002-22000002i3−2i32+2i−2−2i2−2i−2+2i00−2i2i−2323000000−1−i1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−1+i1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000
χ604-4-44-24i−4i002-22000002i3−2i3−2−2i2+2i−2+2i2−2i00−2i2i−23230000001+i−1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221−i−1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000
χ614-4-44-2−4i4i002-2200000−2i32i32−2i−2+2i2+2i−2−2i002i−2i−2323000000−1+i1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−1−i1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000
χ624-4-44-2−4i4i002-2200000−2i32i3−2+2i2−2i−2−2i2+2i002i−2i−23230000001−i−1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ221+i−1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000
χ634-4-44-2−4i4i002-22000002i3−2i32−2i−2+2i2+2i−2−2i002i−2i23−23000000−1+i1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−1−i1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000
χ644-4-44-2−4i4i002-22000002i3−2i3−2+2i2−2i−2−2i2+2i002i−2i23−230000001−i−1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ221+i−1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000
χ6588-8-880000-8-88000000000000000000000000000000000000000000000000000000000
χ6688-8-8-4000044-40000000000043−4300000000000000000000000000000000000000000000
χ6788-8-8-4000044-400000000000−434300000000000000000000000000000000000000000000
χ688-88-8-4008i−8i-44400000000000000000−4i4i00000000000000000000000000000000000000
χ698-88-8-400−8i8i-444000000000000000004i−4i00000000000000000000000000000000000000

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