Finite Group Databasebeta

← Group #11779317

Character table — Group #11779317

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888121224242424242424242424242424363636363636484848484872
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242422224668812122424242422888846612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-1-111-1-11111-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-111-1-11
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111-1-11111-1-1-1-1-1-1
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1111
χ92222222-2-222222222-22222-2-222-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000000022000000000-2
χ102222222-2-222222222-22222-2-222-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000000-2-20000000002
χ11222222-222-22222222-2222-222-2-2222222-200-2-2-2-2-2-200000000000000002200-22200-2-20000000000000000
χ12222222-222-22222222-2222-222-2-2222222-200-2-2-2-2-2-20000000000000000-2-2002-2-200220000000000000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2220000000000000000002-20000000000000000002-2000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000-22000000000000000000-22000
χ1522222-122222-1-1-122-12-1-1-1-12-122-1-12-1-1-1-122-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220002200-1-1-1-10000000-1-1000
χ1622222-122222-1-1-122-12-1-1-1-12-122-1-12-1-1-1-122-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2000-2-2001111000000011000
χ1722222-122222-1-1-122-12-1-1-1-12-122-1-12-1-1-1-1-2-2-12-1-1-1-1-2-2-2-21111111111110022000-2-20011110000000-1-1000
χ1822222-122222-1-1-122-12-1-1-1-12-122-1-12-1-1-1-1-2-2-12-1-1-1-1-2-2-2-211111111111100-2-20002200-1-1-1-1000000011000
χ1922222-1-2-2-2-22-1-1-122-12-1-1-11-21-2-211-2111100-1211-1-10000333333−3−3−3−3−3−3002-2000000033−3−30000000-11000
χ2022222-1-2-2-2-22-1-1-122-12-1-1-11-21-2-211-2111100-1211-1-10000333333−3−3−3−3−3−300-220000000−3−33300000001-1000
χ2122222-1-2-2-2-22-1-1-122-12-1-1-11-21-2-211-2111100-1211-1-10000−3−3−3−3−3−3333333002-20000000−3−3330000000-11000
χ2222222-1-2-2-2-22-1-1-122-12-1-1-11-21-2-211-2111100-1211-1-10000−3−3−3−3−3−333333300-22000000033−3−300000001-1000
χ232222-122222-1222-1-1-12-1-1-12-12-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122002-1-100-1-10000000000200-1-10
χ242222-122222-1222-1-1-12-1-1-12-12-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200-21100110000000000-200110
χ252222-122222-1222-1-1-12-1-1-12-12-1-1-1-1-12-1-12-2-22-1-1-1-1-11111-2-21111-2-2111122002-1-100-1-10000000000-200110
χ262222-122222-1222-1-1-12-1-1-12-12-1-1-1-1-12-1-12-2-22-1-1-1-1-11111-2-21111-2-21111-2-200-21100110000000000200-1-10
χ272222-12-222-2-1222-1-1-1-2-1-1-1-2-1211-1-1-12-1-1-200-211111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i32200-2-1-100110000000000000−i3i30
χ282222-12-222-2-1222-1-1-1-2-1-1-1-2-1211-1-1-12-1-1-200-211111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-20021100-1-10000000000000i3−i30
χ292222-12-222-2-1222-1-1-1-2-1-1-1-2-1211-1-1-12-1-1-200-211111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i32200-2-1-100110000000000000i3−i30
χ302222-12-222-2-1222-1-1-1-2-1-1-1-2-1211-1-1-12-1-1-200-211111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-20021100-1-10000000000000−i3i30
χ3122-2-222200-2-22-2-22-2202-2-22002-2000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000002-2−i2−i2i2i2000000
χ3222-2-222200-2-22-2-22-2202-2-22002-2000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000-22i2i2−i2−i2000000
χ3322-2-222200-2-22-2-22-2202-2-22002-2000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000002-2i2i2−i2−i2000000
χ3422-2-222200-2-22-2-22-2202-2-22002-2000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000-22−i2−i2i2i2000000
χ352-2-222202-202-22-2-2-220-22-20220022-2-2-2-200000000000000000000000002-20002-2−i2i200−i2i2−i2i200−i2i2−i2i2000000
χ362-2-222202-202-22-2-2-220-22-20220022-2-2-2-200000000000000000000000002-20002-2i2−i200i2−i2i2−i200i2−i2i2−i2000000
χ372-2-222202-202-22-2-2-220-22-20220022-2-2-2-20000000000000000000000000-22000-22−i2i200−i2i2−i2i200i2−i2i2−i2000000
χ382-2-222202-202-22-2-2-220-22-20220022-2-2-2-20000000000000000000000000-22000-22i2−i200i2−i2i2−i200−i2i2−i2i2000000
χ3944444-24-4-444-2-2-244-2-4-2-2-2-2-424422-4222-2002-4-2-2220000000000000000000000000000000000000000000
χ4044444-2-444-44-2-2-244-2-4-2-2-224-2-4-4-2-24-2-2-22002-422220000000000000000000000000000000000000000000
χ414444-244-4-44-2444-2-2-2-4-2-2-242-4-2-2222-422400-42-2-2220000000000000000000000000000000000000000000
χ424444-24-4-4-4-4-2444-2-2-24-2-2-2-42-422222-422-4004-222-2-20000000000000000000000000000000000000000000
χ434444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000
χ444444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000
χ454444-2-24-4-44-2-2-2-2-2-21-4111-222-2-2-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000
χ464444-2-24-4-44-2-2-2-2-2-21-4111-222-2-2-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000
χ474444-2-2-444-4-2-2-2-2-2-21-41112-2-22211-2-21120022-1-1-1-1−2i3−2i32i32i300i3i3−i3−i300i3i3−i3−i3000000000000000000000000000
χ484444-2-2-444-4-2-2-2-2-2-21-41112-2-22211-2-21120022-1-1-1-12i32i3−2i3−2i300−i3−i3i3i300−i3−i3i3i3000000000000000000000000000
χ494444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-11100002323−3−3−3−3−23−233333000000000000000000000000000
χ504444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1110000−23−2333332323−3−3−3−3000000000000000000000000000
χ5144-4-444-4004-44-4-44-4404-4-4-400-4400000040000-44000000000000000000000000000000000000000000000
χ5244-4-44-2400-4-4-2224-4-20-222-2004-40000002−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000000
χ5344-4-44-2400-4-4-2224-4-20-222-2004-400000022i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000
χ5444-4-44-2-4004-4-2224-4-20-222200-44000000-200002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000000
χ5544-4-44-2-4004-4-2224-4-20-222200-44000000-200002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000000
χ5644-4-4-24400-424-4-4-22-20-222400-22000000-4−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000000
χ5744-4-4-24400-424-4-4-22-20-222400-22000000-42i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000000
χ5844-4-4-24-400424-4-4-22-20-222-4002-2000000400002-2006−6−66006−6−66006−6−66000000000000000000000000000
χ5944-4-4-24-400424-4-4-22-20-222-4002-2000000400002-200−666−600−666−600−666−6000000000000000000000000000
χ6044-4-4-2-2400-42-222-22101-1-1-200-223i−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−ζ23000000000000000000000000000
χ6144-4-4-2-2400-42-222-22101-1-1-200-223i−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+ζ23000000000000000000000000000
χ6244-4-4-2-2400-42-222-22101-1-1-200-22−3i3i00−3i3i2−2i22i2001-1−3i3ii2−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+2ζ23000000000000000000000000000
χ6344-4-4-2-2400-42-222-22101-1-1-200-22−3i3i00−3i3i22i2−2i2001-1−3i3i−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+ζ13−2ζ23000000000000000000000000000
χ6444-4-4-2-2-40042-222-22101-1-12002-23i−3i003i−3i-20000-11−3i3i6−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ6544-4-4-2-2-40042-222-22101-1-12002-23i−3i003i−3i-20000-11−3i3i−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ6644-4-4-2-2-40042-222-22101-1-12002-2−3i3i00−3i3i-20000-113i−3i6−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ6744-4-4-2-2-40042-222-22101-1-12002-2−3i3i00−3i3i-20000-113i−3i−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ684-44-4440000-4-4-44-4440-4-44000000000000000000000000000000000000000000000000000002-2-22000000
χ694-44-4440000-4-4-44-4440-4-4400000000000000000000000000000000000000000000000000000-222-2000000
χ704-4-44440-4404-44-4-4-440-44-40-4-400-4-444440000000000000000000000000000000000000000000000000000
χ714-4-444-204-4042-22-4-4-202-2204-200-2-2-422200000000000000000000000000000000−2i22i200i2−i2i2−i2000000000000
χ724-4-444-204-4042-22-4-4-202-2204-200-2-2-4222000000000000000000000000000000002i2−2i200−i2i2−i2i2000000000000
χ734-4-444-20-44042-22-4-4-202-220-4200224-2-2-2000000000000000000000000000000000000i6−i6−i6i6000000000000
χ744-4-444-20-44042-22-4-4-202-220-4200224-2-2-2000000000000000000000000000000000000−i6i6i6−i6000000000000
χ754-4-44-2404-40-2-44-422-202-220-2400-2-22-42200000000000000000000000004-4000-2200000000000000000000
χ764-4-44-2404-40-2-44-422-202-220-2400-2-22-4220000000000000000000000000-440002-200000000000000000000
χ774-4-44-240-440-2-44-422-202-2202-40022-24-2-2000000000000000000000000000000000023−230000000000000000
χ784-4-44-240-440-2-44-422-202-2202-40022-24-2-20000000000000000000000000000000000−23230000000000000000
χ798-88-88-40000-844-4-88-4044-4000000000000000000000000000000000000000000000000000000000000000
χ808-88-8-4800004-8-884-4-4044-4000000000000000000000000000000000000000000000000000000000000000
χ818-88-8-4-40000444-44-420-2-22000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000
χ828-88-8-4-40000444-44-420-2-2200000−6i6i006i−6i0000000000000000000000000000000000000000000000000000
χ838-8-88-4-408-80-44-444420-22-20-4-4002244-2-20000000000000000000000000000000000000000000000000000
χ848-8-88-4-40-880-44-444420-22-204400-2-2-4-4220000000000000000000000000000000000000000000000000000

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