Finite Group Databasebeta

← Group #11872288

Character table — Group #11872288

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222224444444444444444444488888888888888888888888121212121212121218181818242424242424242424242424363636364848484872
order1222334466666623466666881212121212121212121266681212122424242424242424242424242424242422444444444422446612121212121244886612128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-1-1-11-1-11-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ51111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1
χ61111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-1111-1-111
χ71111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-11111-1-111-111-11
χ81111111111111111111111-1-11111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1
χ911111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-11-1111-1-111-1-1-1-1111-11-1-1
χ1011111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111
χ1111111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-11
χ1211111111111111-11-1-1-111111-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111111-11-1-1-111-1-111-1-111-11-11-1
χ1311111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111111-11-111-1-111-1-1-1-1-1-1-11-111
χ1411111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1
χ1511111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-111-1
χ1611111111111111-11-1-1-1111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-11-11-1-111-1-111-1-1-1-11-11-11
χ17222222-2-222222222-22222200-2-2-2-2-2-2-2-2-2-22220-2-2-200000000000000000000000022-2-2000000000000-220000000
χ18222222-2-222222222-22222200-2-2-2-2-2-2-2-2-2-22220-2-2-2000000000000000000000000-2-2220000000000002-20000000
χ19222222-2-2222222-222-2-22220022-2-2-2-2-2-2-2-2-2-2-2022200000000000000000000000022-2-20000000000002-20000000
χ20222222-2-2222222-222-2-22220022-2-2-2-2-2-2-2-2-2-2-20222000000000000000000000000-2-222000000000000-220000000
χ2122222-122-122-1-122-1222-1-1-122-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-12222000000002002-1-1-1-1000000000-1-100
χ2222222-122-122-1-122-1222-1-1-122-1-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200000000-200-211110000000001100
χ2322222-122-122-1-122-1222-1-1-1-2-2-1-122-1-1-1-1-1-1-1-1-1-22-1-1-2-2111111-2-2111111222200000000-200-2-1-1-1-10000000001100
χ2422222-122-122-1-122-1222-1-1-1-2-2-1-122-1-1-1-1-1-1-1-1-1-22-1-1-2-2111111-2-2111111-2-2-2-20000000020021111000000000-1-100
χ2522222-122-122-1-12-2-1-2-2-2-1-1-1221122-1-1-1-1-1-1111-2-21122-1-1-1-1-1-1-2-211111122-2-200000000-2002-1-1110000000001-100
χ2622222-122-122-1-12-2-1-2-2-2-1-1-1221122-1-1-1-1-1-1111-2-21122-1-1-1-1-1-1-2-2111111-2-22200000000200-211-1-1000000000-1100
χ2722222-122-122-1-12-2-1-2-2-2-1-1-1-2-21122-1-1-1-1-1-11112-211-2-211111122-1-1-1-1-1-122-2-200000000200-2-1-111000000000-1100
χ2822222-122-122-1-12-2-1-2-2-2-1-1-1-2-21122-1-1-1-1-1-11112-211-2-211111122-1-1-1-1-1-1-2-22200000000-200211-1-10000000001-100
χ292222-12222-1-122-12-12-1-1-1-1-12222-1-122-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100002222000002200000-1-1-1-10000-100-10
χ302222-12222-1-122-12-12-1-1-1-1-12222-1-122-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-200000-2-2000001111000010010
χ312222-12222-1-122-12-12-1-1-1-1-1-2-222-1-122-1-1-1-12-1-1-2-1-1-111-2-2111111-2-211110000222200000-2-200000-1-1-1-1000010010
χ322222-12222-1-122-12-12-1-1-1-1-1-2-222-1-122-1-1-1-12-1-1-2-1-1-111-2-2111111-2-211110000-2-2-2-200000220000011110000-100-10
χ332222-12222-1-122-1-2-1-211-1-1-122-2-2-1-122-1-1-1-1-211-2111-1-122-1-1-1-111-2-21111000022-2-2000002-200000-1-1110000-10010
χ342222-12222-1-122-1-2-1-211-1-1-122-2-2-1-122-1-1-1-1-211-2111-1-122-1-1-1-111-2-211110000-2-22200000-220000011-1-10000100-10
χ352222-12222-1-122-1-2-1-211-1-1-1-2-2-2-2-1-122-1-1-1-1-211211111-2-21111-1-122-1-1-1-1000022-2-200000-2200000-1-1110000100-10
χ362222-12222-1-122-1-2-1-211-1-1-1-2-2-2-2-1-122-1-1-1-1-211211111-2-21111-1-122-1-1-1-10000-2-222000002-20000011-1-10000-10010
χ3722-2-2222-2-22-2-22-202000-2-2200002-22-222-2-200000000000000000000000002-2002i−2i2i−2i2i−2i0000002-2002i−2i000000000
χ3822-2-2222-2-22-2-22-202000-2-2200002-22-222-2-200000000000000000000000002-200−2i2i−2i2i−2i2i0000002-200−2i2i000000000
χ3922-2-2222-2-22-2-22-202000-2-2200002-22-222-2-20000000000000000000000000-22002i−2i−2i2i−2i2i000000-22002i−2i000000000
χ4022-2-2222-2-22-2-22-202000-2-2200002-22-222-2-20000000000000000000000000-2200−2i2i2i−2i2i−2i000000-2200−2i2i000000000
χ4122-2-222-22-22-2-22-202000-2-220000-22-22-2-222000000000000000000000002-2002i−2i002i−2i−2i2i00002-2002i−2i00000000000
χ4222-2-222-22-22-2-22-202000-2-220000-22-22-2-222000000000000000000000002-200−2i2i00−2i2i2i−2i00002-200−2i2i00000000000
χ4322-2-222-22-22-2-22-202000-2-220000-22-22-2-22200000000000000000000000-22002i−2i00−2i2i2i−2i0000-22002i−2i00000000000
χ4422-2-222-22-22-2-22-202000-2-220000-22-22-2-22200000000000000000000000-2200−2i2i002i−2i−2i2i0000-2200−2i2i00000000000
χ4544444-2-4-4-244-2-244-2-444-2-2-20022-4-4222222-2-2-20-4220000000000000000000000000000000000000000000000000
χ4644444-2-4-4-244-2-24-4-24-4-4-2-2-200-2-2-4-422222222204-2-20000000000000000000000000000000000000000000000000
χ474444-24-4-44-2-244-24-2-4-2-2-2-2-200-4-422-4-422224-2-202220000000000000000000000000000000000000000000000000
χ484444-24-4-44-2-244-2-4-2422-2-2-2004422-4-42222-4220-2-2-20000000000000000000000000000000000000000000000000
χ494444-2-244-2-2-2-2-2-2414-2-211144-2-2-2-2-2-21111-2114-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ504444-2-244-2-2-2-2-2-2414-2-2111-4-4-2-2-2-2-2-21111-211-4-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ514444-2-244-2-2-2-2-2-2-41-4221114422-2-2-2-211112-1-1-42-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000
χ524444-2-244-2-2-2-2-2-2-41-422111-4-422-2-2-2-211112-1-142-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000
χ534444-2-2-4-4-2-2-2-2-2-241-4-2-211100222222-1-1-1-1-21102-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ544444-2-2-4-4-2-2-2-2-2-241-4-2-211100222222-1-1-1-1-21102-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000000
χ554444-2-2-4-4-2-2-2-2-2-2-4142211100-2-22222-1-1-1-12-1-10-21100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000000
χ564444-2-2-4-4-2-2-2-2-2-2-4142211100-2-22222-1-1-1-12-1-10-2110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000000
χ5744-4-44-24-424-42-2-40-200022-200004-4-22-2-22200000000000000000000000004-400000000000000-220000000000000
χ5844-4-44-24-424-42-2-40-200022-200004-4-22-2-2220000000000000000000000000-44000000000000002-20000000000000
χ5944-4-44-2-4424-42-2-40-200022-20000-442-222-2-2000000000000000000000004-400000000000000-22000000000000000
χ6044-4-44-2-4424-42-2-40-200022-20000-442-222-2-200000000000000000000000-44000000000000002-2000000000000000
χ6144-4-4-244-4-4-22-4420-200022-20000-224-4-2-222000000000000000000000000000004i−4i00000000000000−2i2i000000000
χ6244-4-4-244-4-4-22-4420-200022-20000-224-4-2-22200000000000000000000000000000−4i4i000000000000002i−2i000000000
χ6344-4-4-24-44-4-22-4420-200022-200002-2-4422-2-20000000000000000000000000004i−4i00000000000000−2i2i00000000000
χ6444-4-4-24-44-4-22-4420-200022-200002-2-4422-2-2000000000000000000000000000−4i4i000000000000002i−2i00000000000
χ654-44-444004-44-4-4-4040004-4-4−2i22i200000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000
χ664-44-444004-44-4-4-4040004-4-42i2−2i2000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000
χ674-44-44-200-2-4422-40-2000-222−2i22i223−23000000000000023−23−2i22i2i2−i2i2−i2i2−i200i6−i6i6−i6i6−i6000000000000000000000000000000000
χ684-44-44-200-2-4422-40-2000-222−2i22i2−23230000000000000−2323−2i22i2i2−i2i2−i2i2−i200−i6i6−i6i6−i6i6000000000000000000000000000000000
χ694-44-44-200-2-4422-40-2000-2222i2−2i223−23000000000000023−232i2−2i2−i2i2−i2i2−i2i200−i6i6−i6i6−i6i6000000000000000000000000000000000
χ704-44-44-200-2-4422-40-2000-2222i2−2i2−23230000000000000−23232i2−2i2−i2i2−i2i2−i2i200i6−i6i6−i6i6−i6000000000000000000000000000000000
χ714-44-4-240042-2-4-420-20−2i32i3-222−2i22i200000000000−2i32i30000i2−i2−2i22i2i2−i2i2−i26−6006−6−66000000000000000000000000000000000
χ724-44-4-240042-2-4-420-20−2i32i3-2222i2−2i200000000000−2i32i30000−i2i22i2−2i2−i2i2−i2i2−6600−666−6000000000000000000000000000000000
χ734-44-4-240042-2-4-420-202i3−2i3-222−2i22i2000000000002i3−2i30000i2−i2−2i22i2i2−i2i2−i2−6600−666−6000000000000000000000000000000000
χ744-44-4-240042-2-4-420-202i3−2i3-2222i2−2i2000000000002i3−2i30000−i2i22i2−2i2−i2i2−i2i26−6006−6−66000000000000000000000000000000000
χ754-44-4-2-200-22-2222010−2i32i31-1-1−2i22i223−2300003i−3i3i−3i0i3−i300−33i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ764-44-4-2-200-22-2222010−2i32i31-1-1−2i22i2−23230000−3i3i−3i3i0i3−i3003−3i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ774-44-4-2-200-22-2222010−2i32i31-1-12i2−2i223−2300003i−3i3i−3i0i3−i300−33−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ784-44-4-2-200-22-2222010−2i32i31-1-12i2−2i2−23230000−3i3i−3i3i0i3−i3003−3−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ794-44-4-2-200-22-22220102i3−2i31-1-1−2i22i223−230000−3i3i−3i3i0−i3i300−33i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ804-44-4-2-200-22-22220102i3−2i31-1-1−2i22i2−232300003i−3i3i−3i0−i3i3003−3i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ814-44-4-2-200-22-22220102i3−2i31-1-12i2−2i223−230000−3i3i−3i3i0−i3i300−33−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ824-44-4-2-200-22-22220102i3−2i31-1-12i2−2i2−232300003i−3i3i−3i0−i3i3003−3−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ834-4-444400-4-4-44-4404000-44-4000000000000000000000000000000000000000000000000000000000000022−2200000
χ844-4-444400-4-4-44-4404000-44-40000000000000000000000000000000000000000000000000000000000000−222200000
χ8588-8-8-4-48-84-444-4402000-2-220000-44-4422-2-200000000000000000000000000000000000000000000000000000000
χ8688-8-8-4-4-884-444-4402000-2-2200004-44-4-2-22200000000000000000000000000000000000000000000000000000000
χ878-8-888-4004-8-8-4480-40004-4400000000000000000000000000000000000000000000000000000000000000000000
χ888-8-88-4800-8448-8-40-40004-4400000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88-4-400444-44-402000-22-2000000006i−6i−6i6i00000000000000000000000000000000000000000000000000000000
χ908-8-88-4-400444-44-402000-22-200000000−6i6i6i−6i00000000000000000000000000000000000000000000000000000000

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