Finite Group Databasebeta

← Group #11785528

Character table — Group #11785528

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1122222444444444444488888888889912121212121212121818181818242424242424242424242424364848484872727272
order12244883366812121212242424246612122424242424244422448888224886688881212242424248242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ511111-1-11111-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-11111-1-111-1-1-1-1-111-1-111-1-1
χ611111-1-11111-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-111-1-111
χ711111-1-11111-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111-1-1-1-111-1-1-1-11111-111-1-1-1-111
χ811111-1-11111-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-111-1-11111-1-1-11111-1-1
χ911-1-11111111-111-1-11111-1-1-11-1-111-1-1111-11-111-1-11-1-1111-1i−ii−i1-111-1-1-1i−ii−ii−ii−i
χ1011-1-11111111-111-1-11111-1-1-11-1-111-1-1111-11-111-1-11-1-1111-1−ii−ii1-111-1-1-1−ii−ii−ii−ii
χ1111-1-11111111-111-1-11111-1-1-11-1-111-1-111-11-11-1-1111-1-111-11i−ii−i-11-1-111-1i−ii−i−ii−ii
χ1211-1-11111111-111-1-11111-1-1-11-1-111-1-111-11-11-1-1111-1-111-11−ii−ii-11-1-111-1−ii−iii−ii−i
χ1311-1-11-1-11111111-1-1-1-1-1-1-1-1-1111-1-111111-11-1-1-1111-1-1-1-11-1i−i−ii1-1-1-1111i−i−iii−i−ii
χ1411-1-11-1-11111111-1-1-1-1-1-1-1-1-1111-1-111111-11-1-1-1111-1-1-1-11-1−iii−i1-1-1-1111−iii−i−iii−i
χ1511-1-11-1-11111111-1-1-1-1-1-1-1-1-1111-1-11111-11-1111-1-11-1-1-1-1-11i−i−ii-1111-1-11i−i−ii−iii−i
χ1611-1-11-1-11111111-1-1-1-1-1-1-1-1-1111-1-11111-11-1111-1-11-1-1-1-1-11−iii−i-1111-1-11−iii−ii−i−ii
χ17222222222222222222222222222222-2-200000000-2-2-2-2-2000000000000-200000000
χ1822222-2-22222-22222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-2-222000000000000200000000
χ19222-2-20022220-2-2-2-2000022-2-20000002200002i−2i2i−2i-2-2200000000002i−2i2i−2i000000000
χ20222-2-20022220-2-2-2-2000022-2-2000000220000−2i2i−2i2i-2-220000000000−2i2i−2i2i000000000
χ21222-2-20022220-2-2-2-2000022-2-2000000-2-22-2-22000022-2002-20000-220000000000000
χ22222-2-20022220-2-2-2-2000022-2-2000000-2-2-222-2000022-200-2200002-20000000000000
χ2322-22-20022220-2-2220000-2-22-20000002200002i−2i−2i2i-22-200000000002i−2i−2i2i000000000
χ2422-22-20022220-2-2220000-2-22-2000000220000−2i2i2i−2i-22-20000000000−2i2i2i−2i000000000
χ2522-22-20022220-2-2220000-2-22-2000000-2-222-2-200002-2200220000-2-20000000000000
χ2622-22-20022220-2-2220000-2-22-2000000-2-2-2-22200002-2200-2-20000220000000000000
χ2722-2-22222222-222-2-22222-2-2-22-2-222-2-2-2-200000000-222-2-2000000000000200000000
χ2822-2-22-2-22222222-2-2-2-2-2-2-2-2-2222-2-222-2-200000000-22222000000000000-200000000
χ2944444441-21-24-2-211-2-2-2-21-2-21-2-211110000000000000000022220000000-1-1-1-10000
χ3044444441-21-24-2-211-2-2-2-21-2-21-2-2111100000000000000000-2-2-2-2000000011110000
χ314444444-21-21411-2-21111-211-211-2-2-2-2002222222200000-1-10000-1-1-1-1-1-1000000000
χ324444444-21-21411-2-21111-211-211-2-2-2-200-2-2-2-2-2-2-2-200000110000111111000000000
χ3344444-4-41-21-2-4-2-21122221-2-2122-1-1-1-10000000000000000022-2-20000000-1-1110000
χ3444444-4-41-21-2-4-2-21122221-2-2122-1-1-1-100000000000000000-2-222000000011-1-10000
χ3544444-4-4-21-21-411-2-2-1-1-1-1-211-2-1-12222002222-2-2-2-200000-1-10000-1-11111000000000
χ3644444-4-4-21-21-411-2-2-1-1-1-1-211-2-1-1222200-2-2-2-222220000011000011-1-1-1-1000000000
χ37444-4-400-21-210-1-1223i3i−3i−3i-21-123i−3i0000002-2-222i−2i2i−2i00000-1100001-1−ii−ii000000000
χ38444-4-400-21-210-1-1223i3i−3i−3i-21-123i−3i000000-222-2−2i2i−2i2i000001-10000-11i−ii−i000000000
χ39444-4-400-21-210-1-122−3i−3i3i3i-21-12−3i3i0000002-2-22−2i2i−2i2i00000-1100001-1i−ii−i000000000
χ40444-4-400-21-210-1-122−3i−3i3i3i-21-12−3i3i000000-222-22i−2i2i−2i000001-10000-11−ii−ii000000000
χ4144-44-400-21-210-1-1-2-23i3i−3i−3i2-112−3i3i00000022-2-22i−2i−2i2i00000-1-1000011−iii−i000000000
χ4244-44-400-21-210-1-1-2-23i3i−3i−3i2-112−3i3i000000-2-222−2i2i2i−2i00000110000-1-1i−i−ii000000000
χ4344-44-400-21-210-1-1-2-2−3i−3i3i3i2-1123i−3i00000022-2-2−2i2i2i−2i00000-1-1000011i−i−ii000000000
χ4444-44-400-21-210-1-1-2-2−3i−3i3i3i2-1123i−3i000000-2-2222i−2i−2i2i00000110000-1-1−iii−i000000000
χ4544-4-44441-21-2-4-2-2-1-1-2-2-2-2-12212211-1-1000000000000000002i−2i2i−2i0000000−ii−ii0000
χ4644-4-44441-21-2-4-2-2-1-1-2-2-2-2-12212211-1-100000000000000000−2i2i−2i2i0000000i−ii−i0000
χ4744-4-4444-21-21-4112211112-1-1-2-1-1-2-222002-22-222-2-200000-110000-11-1-111000000000
χ4844-4-4444-21-21-4112211112-1-1-2-1-1-2-22200-22-22-2-222000001-100001-111-1-1000000000
χ4944-4-44-4-41-21-24-2-2-1-12222-1221-2-2-1-111000000000000000002i−2i−2i2i0000000−iii−i0000
χ5044-4-44-4-41-21-24-2-2-1-12222-1221-2-2-1-11100000000000000000−2i2i2i−2i0000000i−i−ii0000
χ5144-4-44-4-4-21-2141122-1-1-1-12-1-1-21122-2-2002-22-2-2-22200000-110000-1111-1-1000000000
χ5244-4-44-4-4-21-2141122-1-1-1-12-1-1-21122-2-200-22-2222-2-2000001-100001-1-1-111000000000
χ534-400022−2244-4-40000022−2222−2200000022−22004i−4i000000000002i2−2i2000000000000000000000
χ544-400022−2244-4-40000022−2222−2200000022−2200−4i4i00000000000−2i22i2000000000000000000000
χ554-4000−222244-4-400000−2222−2222000000−2222004i−4i00000000000−2i22i2000000000000000000000
χ564-4000−222244-4-400000−2222−2222000000−222200−4i4i000000000002i2−2i2000000000000000000000
χ57888-8-8002-42-4044-2-200002-44-2000000000000000000000000000000000000000000
χ5888-88-8002-42-4044220000-24-4-2000000000000000000000000000000000000000000
χ598-800042−422-4-240006i−6i−2222−22220000002−23i2−3i2000000000000000000000000000000000000
χ608-800042−422-4-24000−6i6i−2222−22220000002−2−3i23i2000000000000000000000000000000000000
χ618-800042−42-424-206i−6i004ζ+2ζ3−4ζ−2ζ3−2ζ−4ζ32ζ+4ζ3000000−222200000000000000000000000000000000000000
χ628-800042−42-424-20−6i6i00−2ζ−4ζ32ζ+4ζ34ζ+2ζ3−4ζ−2ζ3000000−222200000000000000000000000000000000000000
χ638-8000−42422-4-240006i−6i22−2222−22000000−22−3i23i2000000000000000000000000000000000000
χ648-8000−42422-4-24000−6i6i22−2222−22000000−223i2−3i2000000000000000000000000000000000000
χ658-8000−4242-424-206i−6i00−4ζ−2ζ34ζ+2ζ32ζ+4ζ3−2ζ−4ζ300000022−2200000000000000000000000000000000000000
χ668-8000−4242-424-20−6i6i002ζ+4ζ3−2ζ−4ζ3−4ζ−2ζ34ζ+2ζ300000022−2200000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.