Finite Group Databasebeta

← Group #11772822

Character table — Group #11772822

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size11222222244444444888888888888888816161616161616242424242424484848484848484848144144
order122336666346666121224466121212121212121212121266612121212882424242444412121212121288
χ1111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-111-1-11111-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111111-11-1-1-111111111111-1-1-1-1-1-1-1111111-1i−i-1-1ii−i−ii−i
χ611111111111111111-11-1-1-111111111111-1-1-1-1-1-1-1111111-1−ii-1-1−i−iii−ii
χ711111111111111111-11-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11i−i11ii−i−i−ii
χ811111111111111111-11-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11−ii11−i−iiii−i
χ9222222222222222222-2-222-2-22-2-2-2-2-2-222222-2-2-2-200000000000000000
χ1022222222222222222-2-22-2-2-2-22-2-2-2-2-2-222-2-2-2222200000000000000000
χ112222-122-12-12-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-12-1-1-12-1-100000002200-1-1-1-100
χ122222-122-12-12-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-12-1-1-12-1-10000000-2-200111100
χ132222-122-12-12-1-1-1-1222-2-2-1-1-2-2-1111111-1-12-1-11-21100000000000−i3i3−i3i300
χ142222-122-12-12-1-1-1-1222-2-2-1-1-2-2-1111111-1-12-1-11-21100000000000i3−i3i3−i300
χ152222-122-12-12-1-1-1-122-22-21122-1-1-1-1-1-1-1-1-1-2111-21100000002i−2i00−i−iii00
χ162222-122-12-12-1-1-1-122-22-21122-1-1-1-1-1-1-1-1-1-2111-2110000000−2i2i00ii−i−i00
χ172222-122-12-12-1-1-1-122-2-2211-2-2-1111111-1-1-211-12-1-1000000000003−3−3300
χ182222-122-12-12-1-1-1-122-2-2211-2-2-1111111-1-1-211-12-1-100000000000−333−300
χ19222-12-1-12-1-122-1-1-1-1-122222-1-1222-1-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1200-1-1000000
χ20222-12-1-12-1-122-1-1-1-1-122222-1-1222-1-1-1-1-1-1-1-1-12-1-1-1-2-21111-20011000000
χ21222-12-1-12-1-122-1-1-1-1-12-2-222112-2-21111-1-1-1-1-1-211100−i3−i3i3i3000−i3i3000000
χ22222-12-1-12-1-122-1-1-1-1-12-2-222112-2-21111-1-1-1-1-1-211100i3i3−i3−i3000i3−i3000000
χ23222-12-1-12-1-122-1-1-1-1-1-22-2-2-2-1-1222-1-1-1-1-1-1111-211122-1-1-1-1-20011000000
χ24222-12-1-12-1-122-1-1-1-1-1-22-2-2-2-1-1222-1-1-1-1-1-1111-2111-2-21111200-1-1000000
χ25222-12-1-12-1-122-1-1-1-1-1-2-22-2-2112-2-21111-1-11112-1-1-100−i3−i3i3i3000i3−i3000000
χ26222-12-1-12-1-122-1-1-1-1-1-2-22-2-2112-2-21111-1-11112-1-1-100i3i3−i3−i3000−i3i3000000
χ274444444444-44444-4-40000000-4000000-4-4000000000000000000000000
χ284444-244-24-2-4-2-2-2-2-4-4000−2i32i3002000000220−2i32i3000000000000000000000
χ294444-244-24-2-4-2-2-2-2-4-40002i3−2i30020000002202i3−2i3000000000000000000000
χ30444-24-2-24-2-2-44-2-2-22200000−2i32i3-400−2i3−2i32i32i322000000000000000000000000
χ31444-24-2-24-2-2-44-2-2-222000002i3−2i3-4002i32i3−2i3−2i322000000000000000000000000
χ32444-2-2-2-2-2-214-2111-2-2444-2-2-2-2-2-2-2111111-211-2-21100000000000000000
χ33444-2-2-2-2-2-214-2111-2-24-4-4-2-222-222-1-1-1-111-21122-1-100000000000000000
χ34444-2-2-2-2-2-214-2111-2-2-44-422-2-2-2-2-21111112-1-122-1-100000000000000000
χ35444-2-2-2-2-2-214-2111-2-2-4-442222-222-1-1-1-1112-1-1-2-21100000000000000000
χ36444-2-2-2-2-2-21-4-211122000−2i32i3−2i32i3200i3i3−i3−i3-1-10i3−i3003-300000000000000000
χ37444-2-2-2-2-2-21-4-211122000−2i32i32i3−2i3200−i3−i3i3i3-1-10i3−i300-3300000000000000000
χ38444-2-2-2-2-2-21-4-2111220002i3−2i3−2i32i3200i3i3−i3−i3-1-10−i3i300-3300000000000000000
χ39444-2-2-2-2-2-21-4-2111220002i3−2i32i3−2i3200−i3−i3i3i3-1-10−i3i3003-300000000000000000
χ4044-444-4-44440-4-4-4400000000000000000000000002-22-22-200000000000
χ4144-444-4-44440-4-4-440000000000000000000000000-22-22-2200000000000
χ4244-4-24224-2-20-422-2−2i32i300000000000000−2i32i300000002-2−1−i31+i3−1+i31−i300000000000
χ4344-4-24224-2-20-422-2−2i32i300000000000000−2i32i30000000-221+i3−1−i31−i3−1+i300000000000
χ4444-4-24224-2-20-422-22i3−2i3000000000000002i3−2i300000002-2−1+i31−i3−1−i31+i300000000000
χ4544-4-24224-2-20-422-22i3−2i3000000000000002i3−2i30000000-221−i3−1+i31+i3−1−i300000000000
χ4688-88-4-8-8-48-40444-4000000000000000000000000000000000000000000
χ4788-8-4-444-4-4204-2-22−4i34i3000000000000002i3−2i3000000000000000000000000
χ4888-8-4-444-4-4204-2-224i3−4i300000000000000−2i32i3000000000000000000000000
χ498-808800-8-880000-8000000000000000000000000000000000000000000
χ508-808-4004-8-400004000000000023−2323−2323−2300000000000000000000000000
χ518-808-4004-8-4000040000000000−2323−2323−232300000000000000000000000000
χ528-80-48−4i34i3-84-400−4i34i34000000000000000000000000000000000000000000
χ538-80-484i3−4i3-84-4004i3−4i34000000000000000000000000000000000000000000
χ548-80-4-4−4i34i3442002i3−2i3-2000000000023−234ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ1100000000000000000000000000
χ558-80-4-4−4i34i3442002i3−2i3-20000000000−2323−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ1100000000000000000000000000
χ568-80-4-44i3−4i344200−2i32i3-2000000000023−23−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ1100000000000000000000000000
χ578-80-4-44i3−4i344200−2i32i3-20000000000−23232ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ1100000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.