Finite Group Databasebeta

← Group #11921870

Character table — Group #11921870

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222223333446666666666888888881212161616161616161618181818242424242424242424242424242424242424242472727272
order1244234612122244612246688881212366612121212612366612121212888824446612121212121224242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111-1-1-1-111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-1-1111-1-111-1-1-11-111111-1-1-1-11-1-11-1-111-111-1-1111-1-111-1-11-11-111-1-111-1-11111-1-1-1-11-11-1
χ611-1-1-1111-1-111-1-1-11-111111-1-1-1-11-1-11-1-111-111-1-1111-1-111-1-1-11-11-1-111-1-1111111-1-1-1-1-11-11
χ711-1-1-1111-1-111-1-1-11-1111-1-111-1-11-1-11-1-111-111-1-1111-1-1-1-1111-11-111-1-111-1-1-1-1-1-11111-11-11
χ811-1-1-1111-1-111-1-1-11-1111-1-111-1-11-1-11-1-111-111-1-1111-1-1-1-111-11-11-1-111-1-111-1-1-1-111111-11-1
χ922222222222222222222222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222000000000000-1-1-1-1-1-1-1-10000
χ1022222222222222222222-2-2-2-222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2000000000000111111110000
χ1122222-12-1-1-12222-1-122-1-10000-1-122222222-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1000000000000
χ1222222-12-1-1-12222-1-122-1-10000-1-122222222-1-1-1-1-1-1-1-1-1-10000-2-2-2-211111111000000000000
χ132222-22-22222222-2-2-2-2220000222-2-2222-2-2-2-22-2-22-2-2220000000000000000000000000000
χ142222-22-22222222-2-2-2-222000022-111-1-1-111-2-2-111-111-1-1000000000000000033−3−333−3−30000
χ152222-22-22222222-2-2-2-222000022-111-1-1-111-2-2-111-111-1-10000000000000000−3−333−3−3330000
χ162222-2-1-2-1-1-1222211-2-2-1-10000-1-12-2-2222-2-211-111-111-1-100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ172222-2-1-2-1-1-1222211-2-2-1-10000-1-12-2-2222-2-211-111-111-1-100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ1822-2-222-22-2-222-2-22-22-2220000-2-22222-2-2-2-22-22222-2-2-2-20000000000000000000000000000
χ1922-2-222-22-2-222-2-22-22-2220000-2-2-1-1-1-111112-2-1-1-1-11111000000000000000033−3−3−3−3330000
χ2022-2-222-22-2-222-2-22-22-2220000-2-2-1-1-1-111112-2-1-1-1-111110000000000000000−3−33333−3−30000
χ2122-2-22-1-2-11122-2-2-112-2-1-10000112222-2-2-2-2-11-1-1-1-1111100000000−i3i3i3−i3−i3i3i3−i3000000000000
χ2222-2-22-1-2-11122-2-2-112-2-1-10000112222-2-2-2-2-11-1-1-1-1111100000000i3−i3−i3i3i3−i3−i3i3000000000000
χ2322-2-2-2222-2-222-2-2-22-222222-2-2-2-2-111-111-1-1-22-111-1-1-11122-2-2000000000000-1-1-1-111110000
χ2422-2-2-2222-2-222-2-2-22-2222-2-222-2-2-111-111-1-1-22-111-1-1-111-2-2220000000000001111-1-1-1-10000
χ2522-2-2-2-12-11122-2-21-1-22-1-10000112-2-22-2-2221-1-111-1-1-11100002-22-2-1-111-1-111000000000000
χ2622-2-2-2-12-11122-2-21-1-22-1-10000112-2-22-2-2221-1-111-1-1-1110000-22-2211-1-111-1-1000000000000
χ272-22i−2i020-22i−2i2-22i−2i00002-22−2−i2i22i−2i200-22i−2i0000200-2002i−2i2−2−i2i20000000000002−22−2−i2i2−i2i20000
χ282-22i−2i020-22i−2i2-22i−2i00002-22−2−i2i22i−2i-1−i3i31−ii3−300-1−i3i313−3−ii2−2−i2i2000000000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ292-22i−2i020-22i−2i2-22i−2i00002-22−2−i2i22i−2i-1i3−i31−ii−3300-1i3−i31−33−ii2−2−i2i2000000000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ302-22i−2i020-22i−2i2-22i−2i00002-2−22i2−i22i−2i200-22i−2i0000200-2002i−2i−22i2−i2000000000000−22−22i2−i2i2−i20000
χ312-22i−2i020-22i−2i2-22i−2i00002-2−22i2−i22i−2i-1−i3i31−ii3−300-1−i3i313−3−ii−22i2−i2000000000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ322-22i−2i020-22i−2i2-22i−2i00002-2−22i2−i22i−2i-1i3−i31−ii−3300-1i3−i31−33−ii−22i2−i2000000000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ332-2−2i2i020-2−2i2i2-2−2i2i00002-22−2i2−i2−2i2i200-2−2i2i0000200-200−2i2i2−2i2−i20000000000002−22−2i2−i2i2−i20000
χ342-2−2i2i020-2−2i2i2-2−2i2i00002-22−2i2−i2−2i2i-1−i3i31i−i−3300-1−i3i31−33i−i2−2i2−i2000000000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ352-2−2i2i020-2−2i2i2-2−2i2i00002-22−2i2−i2−2i2i-1i3−i31i−i3−300-1i3−i313−3i−i2−2i2−i2000000000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ362-2−2i2i020-2−2i2i2-2−2i2i00002-2−22−i2i2−2i2i200-2−2i2i0000200-200−2i2i−22−i2i2000000000000−22−22−i2i2−i2i20000
χ372-2−2i2i020-2−2i2i2-2−2i2i00002-2−22−i2i2−2i2i-1−i3i31i−i−3300-1−i3i31−33i−i−22−i2i2000000000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ382-2−2i2i020-2−2i2i2-2−2i2i00002-2−22−i2i2−2i2i-1i3−i31i−i3−300-1i3−i313−3i−i−22−i2i2000000000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ393333333333-1-1-1-133-1-1-1-13333-1-100000000-1-100000000-1-1-1-111-1-11111-1-1-1-10000000011-1-1
χ403333333333-1-1-1-133-1-1-1-13333-1-100000000-1-100000000-1-1-1-1-1-111-1-1-1-1111100000000-1-111
χ413333333333-1-1-1-133-1-1-1-1-3-3-3-3-1-100000000-1-100000000111111-1-11111-1-1-1-100000000-1-111
χ423333333333-1-1-1-133-1-1-1-1-3-3-3-3-1-100000000-1-1000000001111-1-111-1-1-1-111110000000011-1-1
χ4333-3-3-3333-3-3-1-111-331-1-1-133-3-311000000001-100000000-1-1111-1-1111-1-1-1-111000000001-1-11
χ4433-3-3-3333-3-3-1-111-331-1-1-133-3-311000000001-100000000-1-111-111-1-1-11111-1-100000000-111-1
χ4533-3-3-3333-3-3-1-111-331-1-1-1-3-33311000000001-10000000011-1-11-1-1111-1-1-1-11100000000-111-1
χ4633-3-3-3333-3-3-1-111-331-1-1-1-3-33311000000001-10000000011-1-1-111-1-1-11111-1-1000000001-1-11
χ4744444-24-2-2-24444-2-244-2-20000-2-2-2-2-2-2-2-2-2-2-2-2111111110000000000000000000000000000
χ484444-4-2-4-2-2-2444422-4-4-2-20000-2-2-222-2-2-222221-1-11-1-1110000000000000000000000000000
χ4944-4-44-2-4-22244-4-4-224-4-2-2000022-2-2-2-22222-221111-1-1-1-10000000000000000000000000000
χ5044-4-4-4-24-22244-4-42-2-44-2-2000022-222-222-2-22-21-1-1111-1-10000000000000000000000000000
χ514-44i−4i0-202−2i2i4-44i−4i0000-220000−2i2i400-44i−4i0000-200200−2i2i0000000000000000000000000000
χ524-44i−4i0-202−2i2i4-44i−4i0000-220000−2i2i-2−2i32i32−2i2i23−23001i3−i3-1−33i−i0000000000000000000000000000
χ534-44i−4i0-202−2i2i4-44i−4i0000-220000−2i2i-22i3−2i32−2i2i−2323001−i3i3-13−3i−i0000000000000000000000000000
χ544-4−4i4i0-2022i−2i4-4−4i4i0000-2200002i−2i400-4−4i4i0000-2002002i−2i0000000000000000000000000000
χ554-4−4i4i0-2022i−2i4-4−4i4i0000-2200002i−2i-2−2i32i322i−2i−2323001i3−i3-13−3−ii0000000000000000000000000000
χ564-4−4i4i0-2022i−2i4-4−4i4i0000-2200002i−2i-22i3−2i322i−2i23−23001−i3i3-1−33−ii0000000000000000000000000000
χ5766666-36-3-3-3-2-2-2-2-3-3-2-211000011000000001100000000000022-2-2-1-1-1-11111000000000000
χ5866666-36-3-3-3-2-2-2-2-3-3-2-2110000110000000011000000000000-2-2221111-1-1-1-1000000000000
χ596666-66-6666-2-2-2-2-6-622-2-20000-2-20000000022000000000000000000000000000000000000
χ606666-6-3-6-3-3-3-2-2-2-233221100001100000000-1-10000000000000000−i3i3−i3i3i3−i3i3−i3000000000000
χ616666-6-3-6-3-3-3-2-2-2-233221100001100000000-1-10000000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ6266-6-666-66-6-6-2-2226-6-22-2-200002200000000-22000000000000000000000000000000000000
χ6366-6-66-3-6-333-2-222-33-22110000-1-1000000001-10000000000000000−i3i3i3−i3i3−i3−i3i3000000000000
χ6466-6-66-3-6-333-2-222-33-22110000-1-1000000001-10000000000000000i3−i3−i3i3−i3i3i3−i3000000000000
χ6566-6-6-6-36-333-2-2223-32-2110000-1-100000000-110000000000002-2-22-1-11111-1-1000000000000
χ6666-6-6-6-36-333-2-2223-32-2110000-1-100000000-11000000000000-222-211-1-1-1-111000000000000
χ676-66i−6i060-66i−6i-22−2i2i0000-2232−32−3i23i2−2i2i000000000000000000−22i2−i2000000000000000000000000
χ686-66i−6i060-66i−6i-22−2i2i0000-22−32323i2−3i2−2i2i0000000000000000002−2−i2i2000000000000000000000000
χ696-6−6i6i060-6−6i6i-222i−2i0000-2232−323i2−3i22i−2i000000000000000000−22−i2i2000000000000000000000000
χ706-6−6i6i060-6−6i6i-222i−2i0000-22−3232−3i23i22i−2i0000000000000000002−2i2−i2000000000000000000000000
χ7112-1212i−12i0-606−6i6i-44−4i4i00002-200002i−2i0000000000000000000000000000000000000000000000
χ7212-12−12i12i0-6066i−6i-444i−4i00002-20000−2i2i0000000000000000000000000000000000000000000000

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