Finite Group Databasebeta

← Group #11781267

Character table — Group #11781267

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222222222244444444444444444888888888888888888888888121212121212121218181818242424242424242436364848484848487272
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242422448888888866121224242424882466121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-111-1-111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1-11111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ92222222-2-222222222-222222-2-2-2222222-200-2-2-2-2-2-2000000000000000022-2-20000000022-2-200000000000000
χ102222222-2-222222222-222222-2-2-2222222-200-2-2-2-2-2-20000000000000000-2-22200000000-2-22200000000000000
χ11222222-222-22222222-2222-2-2222-2-2-2-2-2-2200-2-222-2-2000000000000000000000000222200000000-2-200000000
χ12222222-222-22222222-2222-2-2222-2-2-2-2-2-2200-2-222-2-2000000000000000000000000-2-2-2-2000000002200000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000002i2i−2i−2i000000002i2i−2i−2i0000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-22200000000000000000000−2i−2i2i2i00000000−2i−2i2i2i0000000000
χ1522222-122222-1-1-122-12-1-1-12-1-122-1-12-1-1-1-122-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-10020-1-10000
χ1622222-122222-1-1-122-12-1-1-12-1-122-1-12-1-1-1-122-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111100-20110000
χ1722222-122222-1-1-122-12-1-1-12-1-122-1-12-1-1-1-1-2-2-12-1-1-1-1-2-2-2-21111111111110000222200000000-1-1-1-100-20110000
χ1822222-122222-1-1-122-12-1-1-12-1-122-1-12-1-1-1-1-2-2-12-1-1-1-1-2-2-2-21111111111110000-2-2-2-20000000011110020-1-10000
χ1922222-1-2-2-2-22-1-1-122-12-1-1-1-211-2-211-2111100-1211-1-10000333333−3−3−3−3−3−300002i2i−2i−2i00000000−i−iii0000−i3i30000
χ2022222-1-2-2-2-22-1-1-122-12-1-1-1-211-2-211-2111100-1211-1-10000333333−3−3−3−3−3−30000−2i−2i2i2i00000000ii−i−i0000i3−i30000
χ2122222-1-2-2-2-22-1-1-122-12-1-1-1-211-2-211-2111100-1211-1-10000−3−3−3−3−3−333333300002i2i−2i−2i00000000−i−iii0000i3−i30000
χ2222222-1-2-2-2-22-1-1-122-12-1-1-1-211-2-211-2111100-1211-1-10000−3−3−3−3−3−33333330000−2i−2i2i2i00000000ii−i−i0000−i3i30000
χ232222-122222-1222-1-1-12-1-1-1-122-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1222200000000-1-1-1-10000000200-1-100
χ242222-122222-1222-1-1-12-1-1-1-122-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20000000011110000000-2001100
χ252222-122222-1222-1-1-12-1-1-1-122-1-1-1-1-12-1-12-2-22-1-1-1-1-11111-2-21111-2-21111222200000000-1-1-1-10000000-2001100
χ262222-122222-1222-1-1-12-1-1-1-122-1-1-1-1-12-1-12-2-22-1-1-1-1-11111-2-21111-2-21111-2-2-2-20000000011110000000200-1-100
χ272222-122-2-22-1222-1-1-1-2-1-1-1-12-211-1-1-12-1-1-200-211111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i322-2-200000000-1-1110000000000−i3i300
χ282222-122-2-22-1222-1-1-1-2-1-1-1-12-211-1-1-12-1-1-200-211111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-2220000000011-1-10000000000i3−i300
χ292222-122-2-22-1222-1-1-1-2-1-1-1-12-211-1-1-12-1-1-200-211111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i322-2-200000000-1-1110000000000i3−i300
χ302222-122-2-22-1222-1-1-1-2-1-1-1-12-211-1-1-12-1-1-200-211111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-2220000000011-1-10000000000−i3i300
χ3122-2-222200-222-2-2-2-2202-2-2-2-2000-2-222220000000000000000000000000002i−2i2−22−2−i2−i2i2i2002i−2i2−22−2−i2i200000000
χ3222-2-222200-222-2-2-2-2202-2-2-2-2000-2-222220000000000000000000000000002i−2i−22−22i2i2−i2−i2002i−2i−22−22i2−i200000000
χ3322-2-222200-222-2-2-2-2202-2-2-2-2000-2-22222000000000000000000000000000−2i2i2−22−2i2i2−i2−i200−2i2i2−22−2i2−i200000000
χ3422-2-222200-222-2-2-2-2202-2-2-2-2000-2-22222000000000000000000000000000−2i2i−22−22−i2−i2i2i200−2i2i−22−22−i2i200000000
χ3522-2-222-200222-2-2-2-2202-2-22200022-2-2-2-200000000000000000000000002-200−i2i2i2−i2−i2−i2i2i22-200−i2i2i2−i2i2−i200000000
χ3622-2-222-200222-2-2-2-2202-2-22200022-2-2-2-200000000000000000000000002-200i2−i2−i2i2i2i2−i2−i22-200i2−i2−i2i2−i2i200000000
χ3722-2-222-200222-2-2-2-2202-2-22200022-2-2-2-20000000000000000000000000-2200−i2i2i2−i2i2i2−i2−i2-2200−i2i2i2−i2−i2i200000000
χ3822-2-222-200222-2-2-2-2202-2-22200022-2-2-2-20000000000000000000000000-2200i2−i2−i2i2−i2−i2i2i2-2200i2−i2−i2i2i2−i200000000
χ392-22-22202-20-2-22-22-220-22-20022-2000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000002i−2i2i−2i00000000000000002−2
χ402-22-22202-20-2-22-22-220-22-20022-2000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000−2i2i−2i2i0000000000000000−22
χ412-22-22202-20-2-22-22-220-22-20022-2000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000002i−2i2i−2i0000000000000000−22
χ422-22-22202-20-2-22-22-220-22-20022-2000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000−2i2i−2i2i00000000000000002−2
χ4344444-24-4-444-2-2-244-2-4-2-2-24-22-4-4-2-24-2-2-22002-422220000000000000000000000000000000000000000000000
χ4444444-2-444-44-2-2-244-2-4-2-2-2-42-24422-4222-2002-4-2-2220000000000000000000000000000000000000000000000
χ454444-24-444-4-2444-2-2-2-4-2-2-22-44-2-2222-422400-42-2-2220000000000000000000000000000000000000000000000
χ464444-24-4-4-4-4-2444-2-2-24-2-2-22-4-422222-422-4004-222-2-20000000000000000000000000000000000000000000000
χ474444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000000
χ484444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000000
χ494444-2-24-4-44-2-2-2-2-2-21-4111-2-222211-2-21120022-1-1-1-1−2i3−2i32i32i300i3i3−i3−i300i3i3−i3−i3000000000000000000000000000000
χ504444-2-24-4-44-2-2-2-2-2-21-4111-2-222211-2-21120022-1-1-1-12i32i3−2i3−2i300−i3−i3i3i300−i3−i3i3i3000000000000000000000000000000
χ514444-2-2-444-4-2-2-2-2-2-21-411122-2-2-2-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000000
χ524444-2-2-444-4-2-2-2-2-2-21-411122-2-2-2-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000000
χ534444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-11100002323−3−3−3−3−23−233333000000000000000000000000000000
χ544444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1110000−23−2333332323−3−3−3−3000000000000000000000000000000
χ5544-4-44-2400-44-222-4-4-20-222-42000224-2-2-20000000000000000000000000000022−2222−2200000000−22−220000000000
χ5644-4-44-2400-44-222-4-4-20-222-42000224-2-2-200000000000000000000000000000−2222−2222000000002−22−20000000000
χ5744-4-44-2-40044-222-4-4-20-2224-2000-2-2-422200000000000000000000000000000−2i22i22i2−2i200000000i2−i2−i2i20000000000
χ5844-4-44-2-40044-222-4-4-20-2224-2000-2-2-4222000000000000000000000000000002i2−2i2−2i22i200000000−i2i2i2−i20000000000
χ5944-4-4-24400-4-24-4-422-20-2222-400022-24-2-20000000000000000000000000004i−4i0000000000−2i2i00000000000000
χ6044-4-4-24400-4-24-4-422-20-2222-400022-24-2-2000000000000000000000000000−4i4i00000000002i−2i00000000000000
χ6144-4-4-24-4004-24-4-422-20-222-24000-2-22-42200000000000000000000000004-40000000000-220000000000000000
χ6244-4-4-24-4004-24-4-422-20-222-24000-2-22-4220000000000000000000000000-4400000000002-20000000000000000
χ634-44-4440-440-4-44-44-440-44-400-4-4400000040000-44000000000000000000000000000000000000000000000000
χ644-44-44-204-40-42-224-4-202-2200-24-40000002−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000
χ654-44-44-204-40-42-224-4-202-2200-24-400000022i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000
χ664-44-44-20-440-42-224-4-202-22002-44000000-200002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000000000
χ674-44-44-20-440-42-224-4-202-22002-44000000-200002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000000000
χ684-44-4-2404-402-44-4-22-202-22004-22000000-4−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000000000
χ694-44-4-2404-402-44-4-22-202-22004-22000000-42i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000000000
χ704-44-4-240-4402-44-4-22-202-2200-42-2000000400002-2006−6−66006−6−66006−6−66000000000000000000000000000000
χ714-44-4-240-4402-44-4-22-202-2200-42-2000000400002-200−666−600−666−600−666−6000000000000000000000000000000
χ724-44-4-2-204-4022-22-2210-11-100-2-223i−3i003i−3i2−2i22i2001-13i−3ii2−i2i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23000000000000000000000000000000
χ734-44-4-2-204-4022-22-2210-11-100-2-223i−3i003i−3i22i2−2i2001-13i−3i−i2i2−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000000000
χ744-44-4-2-204-4022-22-2210-11-100-2-22−3i3i00−3i3i2−2i22i2001-1−3i3ii2−i2i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23000000000000000000000000000000
χ754-44-4-2-204-4022-22-2210-11-100-2-22−3i3i00−3i3i22i2−2i2001-1−3i3i−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000000000000
χ764-44-4-2-20-44022-22-2210-11-10022-23i−3i003i−3i-20000-11−3i3i6−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ774-44-4-2-20-44022-22-2210-11-10022-23i−3i003i−3i-20000-11−3i3i−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ784-44-4-2-20-44022-22-2210-11-10022-2−3i3i00−3i3i-20000-113i−3i6−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ794-44-4-2-20-44022-22-2210-11-10022-2−3i3i00−3i3i-20000-113i−3i−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ804-4-44440000-4-4-44-4440-4-440000000000000000000000000000000000000000000022−22−2222000000000000000000
χ814-4-44440000-4-4-44-4440-4-4400000000000000000000000000000000000000000000−222222−22000000000000000000
χ8288-8-8-4-4800-8-4-44444202-2-244000-2-2-4-4220000000000000000000000000000000000000000000000000000000
χ8388-8-8-4-4-8008-4-44444202-2-2-4-40002244-2-20000000000000000000000000000000000000000000000000000000
χ848-8-888-40000-844-4-88-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ858-8-88-4800004-8-884-4-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-4-40000444-44-420-2-22000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000000
χ878-8-88-4-40000444-44-420-2-2200000−6i6i006i−6i0000000000000000000000000000000000000000000000000000000

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