Finite Group Databasebeta

← Group #11776358

Character table — Group #11776358

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222444444444444444444444888888888888888888888818181818181824242424242424242424242424242424363636363648484848
order1222334444666666346668888121212121212121212121212121212121212242424242424242424242424242424242244444444888824242424242424244888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111
χ5111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ6111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1
χ8111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11111-1-111
χ9111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1111-11-1i−ii−iii−i−iii−i−i-1ii−i−i1-11-1
χ10111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-11-11−ii−ii−i−iii−i−iii-1ii−i−i-11-11
χ11111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11-1-11i−i−iiii−i−i−i−iii1−i−iii1-1-11
χ12111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-111-1−iii−i−i−iiiii−i−i1−i−iii-111-1
χ13111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1111-11-1−ii−ii−i−iii−i−iii-1−i−iii1-11-1
χ14111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-11-11i−ii−iii−i−iii−i−i-1−i−iii-11-11
χ15111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11-1-11−iii−i−i−iiiii−i−i1ii−i−i1-1-11
χ16111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-111-1i−i−iiii−i−i−i−iii1ii−i−i-111-1
χ172222222-22-22222222-2222000022-2-2-2-2-2-2-2-222-2-2-2-22200000000000000002222-2-20000000000000000-200000000
χ182222222-22-22222222-2222000022-2-2-2-2-2-2-2-222-2-2-2-2220000000000000000-2-2-2-2220000000000000000200000000
χ19222222-22-222222222-22220000-2-222222222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-20000000000000000200000000
χ20222222-22-222222222-22220000-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-222220000000000000000-200000000
χ2122222-1222222-1-12-1-12-1-1-122222-12-1-1-12-1-1-12-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000002200220000-1-1-1-10000000-1-1
χ2222222-1222222-1-12-1-12-1-1-122222-12-1-1-12-1-1-12-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000-2-200-2-200001111000000011
χ2322222-1222222-1-12-1-12-1-1-1-2-2-2-22-12-1-1-12-1-1-12-12-1-1-1-1-1-2-2111111-2-2111111000000002200-2-2000011110000000-1-1
χ2422222-1222222-1-12-1-12-1-1-1-2-2-2-22-12-1-1-12-1-1-12-12-1-1-1-1-1-2-2111111-2-211111100000000-2-200220000-1-1-1-1000000011
χ2522222-1-2-2-2-222-1-12-1-12-1-1-12i2i−2i−2i-21-2111-2111-212-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii000000002-2002i−2i0000−i−iii0000000-11
χ2622222-1-2-2-2-222-1-12-1-12-1-1-12i2i−2i−2i-21-2111-2111-212-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00000000-2200−2i2i0000ii−i−i00000001-1
χ2722222-1-2-2-2-222-1-12-1-12-1-1-1−2i−2i2i2i-21-2111-2111-212-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i000000002-200−2i2i0000ii−i−i0000000-11
χ2822222-1-2-2-2-222-1-12-1-12-1-1-1−2i−2i2i2i-21-2111-2111-212-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000-22002i−2i0000−i−iii00000001-1
χ292222-122222-1-122-12-12-1-1-12222-12-12-1-1-12-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000022002200-1-1-1-1000000000-1-100
χ302222-122222-1-122-12-12-1-1-12222-12-12-1-1-12-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000-2-200-2-20011110000000001100
χ312222-122222-1-122-12-12-1-1-1-2-2-2-2-12-12-1-1-12-1-1-12-12-1-1-1-111-2-2111111-2-211110000002200-2-2001111000000000-1-100
χ322222-122222-1-122-12-12-1-1-1-2-2-2-2-12-12-1-1-12-1-1-12-12-1-1-1-111-2-2111111-2-21111000000-2-2002200-1-1-1-10000000001100
χ332222-12-2-2-2-2-1-122-12-12-1-1-12i2i−2i−2i1-21-2111-2111-2-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii0000002-2002i−2i00−i−iii000000000-1100
χ342222-12-2-2-2-2-1-122-12-12-1-1-12i2i−2i−2i1-21-2111-2111-2-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii000000-2200−2i2i00ii−i−i0000000001-100
χ352222-12-2-2-2-2-1-122-12-12-1-1-1−2i−2i2i2i1-21-2111-2111-2-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i0000002-200−2i2i00ii−i−i000000000-1100
χ362222-12-2-2-2-2-1-122-12-12-1-1-1−2i−2i2i2i1-21-2111-2111-2-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i000000-22002i−2i00−i−iii0000000001-100
χ3722-2-22220-202-22-2-2-2202-2-22−22−22200000000-2-200002-22−22−222−2−22−22−222−2−22-22-200000000000000000002−22−20000
χ3822-2-22220-202-22-2-2-2202-2-22−22−22200000000-2-200002-22−22−222−2−22−22−222−2−2-22-220000000000000000000−22−220000
χ3922-2-22220-202-22-2-2-2202-2-2−22−222200000000-2-200002-2−22−22−2−222−22−22−2−2222-22-20000000000000000000−22−220000
χ4022-2-22220-202-22-2-2-2202-2-2−22−222200000000-2-200002-2−22−22−2−222−22−22−2−222-22-2200000000000000000002−22−20000
χ4122-2-222-20202-22-2-2-2202-2-2−i2i2i2−i2-2-200000000220000-22−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i22-2-220000000000000000000−i2i2i2−i20000
χ4222-2-222-20202-22-2-2-2202-2-2−i2i2i2−i2-2-200000000220000-22−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i2-222-20000000000000000000i2−i2−i2i20000
χ4322-2-222-20202-22-2-2-2202-2-2i2−i2−i2i2-2-200000000220000-22i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i22-2-220000000000000000000i2−i2−i2i20000
χ4422-2-222-20202-22-2-2-2202-2-2i2−i2−i2i2-2-200000000220000-22i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2-222-20000000000000000000−i2i2i2−i20000
χ4544444-24-44-444-2-24-2-2-4-2-2-200004-2-4222-42224-2-4222-2-200000000000000000000000000000000000000000000000
χ4644444-2-44-4444-2-24-2-2-4-2-2-20000-424-2-2-24-2-2-2-42-42222200000000000000000000000000000000000000000000000
χ474444-244-44-4-2-244-24-2-4-2-2-20000-242-4222-422-242-422-2-200000000000000000000000000000000000000000000000
χ484444-24-44-44-2-244-24-2-4-2-2-200002-4-24-2-2-24-2-22-42-4222200000000000000000000000000000000000000000000000
χ494444-2-24444-2-2-2-2-2-2141114444-2-2-2-211-2-211-2-2-2-21111-2-2-2-21111-2-2-2-211110000000000000000000000000000000
χ504444-2-24444-2-2-2-2-2-214111-4-4-4-4-2-2-2-211-2-211-2-2-2-211112222-1-1-1-12222-1-1-1-10000000000000000000000000000000
χ514444-2-24-44-4-2-2-2-2-2-21-41110000-2-222-1-122-1-1-2-222-1-11100003i−3i3i−3i00003i−3i3i−3i0000000000000000000000000000000
χ524444-2-24-44-4-2-2-2-2-2-21-41110000-2-222-1-122-1-1-2-222-1-1110000−3i3i−3i3i0000−3i3i−3i3i0000000000000000000000000000000
χ534444-2-2-44-44-2-2-2-2-2-21-4111000022-2-211-2-2112222-1-1-1-100003-33-30000-33-330000000000000000000000000000000
χ544444-2-2-44-44-2-2-2-2-2-21-4111000022-2-211-2-2112222-1-1-1-10000-33-3300003-33-30000000000000000000000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-2141114i4i−4i−4i2222-1-122-1-122-2-211-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-214111−4i−4i4i4i2222-1-122-1-122-2-211-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000000
χ5744-4-44-240-404-4-22-42-20-22222−2222−224-200000000-420000-2222−22−22−2−22222−22−22−2−2220000000000000000000000000000000
χ5844-4-44-240-404-4-22-42-20-222−2222−22224-200000000-420000-22−22222−222−2−2−22222−222−2−20000000000000000000000000000000
χ5944-4-44-2-40404-4-22-42-20-222−2i22i22i2−2i2-42000000004-200002-2−2i22i2i2−i2i2i2−i2−i22i2−2i2−i2i2−i2−i2i2i20000000000000000000000000000000
χ6044-4-44-2-40404-4-22-42-20-2222i2−2i2−2i22i2-42000000004-200002-22i2−2i2−i2i2−i2−i2i2i2−2i22i2i2−i2i2i2−i2−i20000000000000000000000000000000
χ6144-4-4-2440-40-224-42-4-20-22222−2222−22-24000000002-40000-22−2222−22−2−222−2222−22−2−2220000000000000000000000000000000
χ6244-4-4-2440-40-224-42-4-20-222−2222−2222-24000000002-40000-222−2−222222−2−22−2−222222−2−20000000000000000000000000000000
χ6344-4-4-24-4040-224-42-4-20-222−2i22i22i2−2i22-400000000-2400002-2i2−i2−2i22i2i2i2−i2−i2−i2i22i2−2i2−i2−i2i2i20000000000000000000000000000000
χ6444-4-4-24-4040-224-42-4-20-2222i2−2i2−2i22i22-400000000-2400002-2−i2i22i2−2i2−i2−i2i2i2i2−i2−2i22i2i2i2−i2−i20000000000000000000000000000000
χ6544-4-4-2-240-40-22-2222101-1-122−2222−22-2-2003i−3i003i−3i22003i−3i1-1−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ230000000000000000000000000000000
χ6644-4-4-2-240-40-22-2222101-1-122−2222−22-2-200−3i3i00−3i3i2200−3i3i1-1−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ230000000000000000000000000000000
χ6744-4-4-2-240-40-22-2222101-1-1−2222−2222-2-2003i−3i003i−3i22003i−3i1-12−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ230000000000000000000000000000000
χ6844-4-4-2-240-40-22-2222101-1-1−2222−2222-2-200−3i3i00−3i3i2200−3i3i1-12−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ230000000000000000000000000000000
χ6944-4-4-2-2-4040-22-2222101-1-1−2i22i22i2−2i222003i−3i003i−3i-2-200−3i3i-11i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ230000000000000000000000000000000
χ7044-4-4-2-2-4040-22-2222101-1-1−2i22i22i2−2i22200−3i3i00−3i3i-2-2003i−3i-11i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ230000000000000000000000000000000
χ7144-4-4-2-2-4040-22-2222101-1-12i2−2i2−2i22i222003i−3i003i−3i-2-200−3i3i-11−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ230000000000000000000000000000000
χ7244-4-4-2-2-4040-22-2222101-1-12i2−2i2−2i22i22200−3i3i00−3i3i-2-2003i−3i-11−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ230000000000000000000000000000000
χ734-44-444040-4-44-44-4-440-44-4000000-4-4-4-444440000000000000000000000000000000000000000000000000000000
χ744-44-4440-404-44-44-4-440-44-40000004444-4-4-4-40000000000000000000000000000000000000000000000000000000
χ754-44-44-2040-4-442-2-42-202-22000000-42224-2-2-20000000000000000000000000000000000000000006−66−6000000000
χ764-44-44-2040-4-442-2-42-202-22000000-42224-2-2-2000000000000000000000000000000000000000000−66−66000000000
χ774-44-44-20-404-442-2-42-202-220000004-2-2-2-4222000000000000000000000000000000000000000000i6−i6−i6i6000000000
χ784-44-44-20-404-442-2-42-202-220000004-2-2-2-4222000000000000000000000000000000000000000000−i6i6i6−i6000000000
χ794-44-4-24040-42-2-442-4-202-220000002-422-24-2-2000000000000000000000000000000000000006−66−60000000000000
χ804-44-4-24040-42-2-442-4-202-220000002-422-24-2-200000000000000000000000000000000000000−66−660000000000000
χ814-44-4-240-4042-2-442-4-202-22000000-24-2-22-42200000000000000000000000000000000000000i6−i6−i6i60000000000000
χ824-44-4-240-4042-2-442-4-202-22000000-24-2-22-42200000000000000000000000000000000000000−i6i6i6−i60000000000000
χ834-4-44440000-4-4-4-44440-4-440000000000000000000000000000000000000000004-40000000000000000000000000
χ844-4-44440000-4-4-4-44440-4-44000000000000000000000000000000000000000000-440000000000000000000000000
χ858-88-8-4-4080-84-44-44420-22-200000044-2-2-4-4220000000000000000000000000000000000000000000000000000000
χ868-88-8-4-40-8084-44-44420-22-2000000-4-42244-2-20000000000000000000000000000000000000000000000000000000
χ878-8-888-40000-8-8448-4-4044-4000000000000000000000000000000000000000000000000000000000000000000000
χ888-8-88-48000044-8-8-48-4044-4000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88-4-400004444-4-420-2-22000000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000000
χ908-8-88-4-400004444-4-420-2-2200000000−6i6i006i−6i0000000000000000000000000000000000000000000000000000000

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