Finite Group Databasebeta

← Group #11711050

Character table — Group #11711050

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222444466668888888812121212121212121212161616161616161616161616242424242424242424244848
order122244442244224444443666121212124488888888666666121212121212444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11-1iiii−i−i−i−i-1-1111111-1-1-1-11-1ii−i−iii−i−ii−i
χ61111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11-1−i−i−i−iiiii-1-1111111-1-1-1-11-1−i−iii−i−iii−ii
χ71111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1iiii−i−i−i−i-1-1-1-1-1-1111111-11ii−i−i−i−iii−ii
χ81111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1−i−i−i−iiiii-1-1-1-1-1-1111111-11−i−iiiii−i−ii−i
χ922222222222222222222-1-1-1-1-1-1-1-12200000000-1-1-1-1-1-1-1-1-1-1-1-1220000000000
χ10222222222222-2-2-2-22222-1-1-1-1-1-1-1-12200000000-1-11111-1-11111-2-20000000000
χ1122222222-2-2-2-20000222222222222-2-200000000-2-20000-2-20000000000000000
χ1222222222-2-2-2-200002222-1-1-1-1-1-1-1-1-2-20000000011−i3−i3i3i311−i3−i3i3i3000000000000
χ1322222222-2-2-2-200002222-1-1-1-1-1-1-1-1-2-20000000011i3i3−i3−i311i3i3−i3−i3000000000000
χ142222-2-2-2-222-2-2000022-2-22222-2-2-2-2-2200000000220000-2-20000000000000000
χ152222-2-2-2-222-2-2000022-2-2-1-1-1-11111-2200000000-1-1−i3−i3i3i311i3i3−i3−i3000000000000
χ162222-2-2-2-222-2-2000022-2-2-1-1-1-11111-2200000000-1-1i3i3−i3−i311−i3−i3i3i3000000000000
χ172222-2-2-2-2-2-22222-2-222-2-2-1-1-1-111112-20000000011-1-1-1-1-1-111112-20000000000
χ182222-2-2-2-2-2-222-2-22222-2-2-1-1-1-111112-200000000111111-1-1-1-1-1-1-220000000000
χ1922-2-222-2-22-22-22-22-20000-111-111-1-10022−2−222−2−21-11-11-11-11-11-10000002−22−200
χ2022-2-222-2-22-22-22-22-20000-111-111-1-100−2−222−2−2221-11-11-11-11-11-1000000−22−2200
χ2122-2-222-2-22-22-2-22-220000-111-111-1-10022−2−222−2−21-1-11-111-1-11-11000000−22−2200
χ2222-2-222-2-22-22-2-22-220000-111-111-1-100−2−222−2−2221-1-11-111-1-11-110000002−22−200
χ2322-2-2-2-222-222-22-2-220000-111-1-1-11100−i2−i2i2i2i2i2−i2−i2-111-11-11-1-11-11000000−i2i2i2−i200
χ2422-2-2-2-222-222-22-2-220000-111-1-1-11100i2i2−i2−i2−i2−i2i2i2-111-11-11-1-11-11000000i2−i2−i2i200
χ2522-2-2-2-222-222-2-222-20000-111-1-1-11100−i2−i2i2i2i2i2−i2−i2-11-11-111-11-11-1000000i2−i2−i2i200
χ2622-2-2-2-222-222-2-222-20000-111-1-1-11100i2i2−i2−i2−i2−i2i2i2-11-11-111-11-11-1000000−i2i2i2−i200
χ272-22-22i−2i2i−2i000000002-22i−2i22-2-22i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i000000
χ282-22-22i−2i2i−2i000000002-22i−2i22-2-22i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i000000
χ292-22-2−2i2i−2i2i000000002-2−2i2i22-2-2−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i000000
χ302-22-2−2i2i−2i2i000000002-2−2i2i22-2-2−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i000000
χ313333333333333333-1-1-1-100000000-1-111111111000000000000-1-1-1-1-1-11111-1-1
χ323333333333333333-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-1-11111-1-1-1-111
χ33333333333333-3-3-3-3-1-1-1-100000000-1-11111111100000000000011-1-1-1-1-1-1-1-111
χ34333333333333-3-3-3-3-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000001111111111-1-1
χ353333-3-3-3-3-3-33333-3-3-1-11100000000-11iiii−i−i−i−i000000000000-11−i−iiiii−i−i−ii
χ363333-3-3-3-3-3-33333-3-3-1-11100000000-11−i−i−i−iiiii000000000000-11ii−i−i−i−iiii−i
χ373333-3-3-3-3-3-333-3-333-1-11100000000-11iiii−i−i−i−i0000000000001-1−i−iii−i−iiii−i
χ383333-3-3-3-3-3-333-3-333-1-11100000000-11−i−i−i−iiiii0000000000001-1ii−i−iii−i−i−ii
χ3944-4-444-4-44-44-44-44-400001-1-11-1-1110000000000-11-11-11-11-11-11000000000000
χ4044-4-444-4-44-44-4-44-4400001-1-11-1-1110000000000-111-11-1-111-11-1000000000000
χ4144-4-444-4-4-44-44000000001-1-11-1-11100000000001-1−i3i3i3−i31-1−i3i3i3−i3000000000000
χ4244-4-444-4-4-44-44000000001-1-11-1-11100000000001-1i3−i3−i3i31-1i3−i3−i3i3000000000000
χ4344-4-444-4-4-44-4400000000-222-222-2-20000000000-220000-220000000000000000
χ4444-4-4-4-4444-4-44000000001-1-1111-1-10000000000-11−i3i3i3−i31-1i3−i3−i3i3000000000000
χ4544-4-4-4-4444-4-44000000001-1-1111-1-10000000000-11i3−i3−i3i31-1−i3i3i3−i3000000000000
χ4644-4-4-4-4444-4-4400000000-222-2-2-22200000000002-20000-220000000000000000
χ4744-4-4-4-444-444-44-4-4400001-1-1111-1-100000000001-1-11-11-111-11-1000000000000
χ4844-4-4-4-444-444-4-444-400001-1-1111-1-100000000001-11-11-1-11-11-11000000000000
χ494-44-44i−4i4i−4i000000004-44i−4i-2-222−2i2i−2i2i0000000000000000000000000000000000
χ504-44-4−4i4i−4i4i000000004-4−4i4i-2-2222i−2i2i−2i0000000000000000000000000000000000
χ514-4-444i−4i−4i4i000000000000-22-222i−2i−2i2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ524-4-444i−4i−4i4i000000000000-22-222i−2i−2i2i00−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ534-4-44−4i4i4i−4i000000000000-22-22−2i2i2i−2i00−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ544-4-44−4i4i4i−4i000000000000-22-22−2i2i2i−2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ5566666666-6-6-6-60000-2-2-2-2000000002200000000000000000000000000000000
χ566666-6-6-6-666-6-60000-2-222000000002-200000000000000000000000000000000
χ576-66-66i−6i6i−6i00000000-22−2i2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i000000
χ586-66-66i−6i6i−6i00000000-22−2i2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i000000
χ596-66-6−6i6i−6i6i00000000-222i−2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i000000
χ606-66-6−6i6i−6i6i00000000-222i−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i000000
χ618-8-888i−8i−8i8i0000000000002-22-2−2i2i2i−2i0000000000000000000000000000000000
χ628-8-88−8i8i8i−8i0000000000002-22-22i−2i−2i2i0000000000000000000000000000000000

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