Finite Group Databasebeta

← Group #11780997

Character table — Group #11780997

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222444444444444444444444888888888888888888888818181818242424242424242424242424363636363636484848484848
order1222334444666666346668888121212121212121212121212121212121212242424242424242424242424242424248888888824242424242424244444884412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-111
χ5111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-11-1-111
χ8111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-111-1-1
χ92222222-2-222222222-2222000022-2-2-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000022-2-200000000
χ102222222-2-222222222-2222000022-2-2-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000-2-22200000000
χ11222222-222-22222222-22220000-2-222222222-2-2-2-2-2-2-2-2000000000000000022220000000000000000-2-2000000
χ12222222-222-22222222-22220000-2-222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2000000000000000022000000
χ13222222-2-2-2-2222222222222i2i−2i−2i-2-2-2-2-2-2-2-2-2-2-2-222-2-2222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i0000000000000000000000000000
χ14222222-2-2-2-222222222222−2i−2i2i2i-2-2-2-2-2-2-2-2-2-2-2-222-2-222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i0000000000000000000000000000
χ1522222-1222222-1-12-1-12-1-1-122222-12-1-1-12-1-1-12-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000220000-1-1-1-10000000200-1-1
χ1622222-1222222-1-12-1-12-1-1-122222-12-1-1-12-1-1-12-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000-2-2000011110000000-20011
χ1722222-1222222-1-12-1-12-1-1-1-2-2-2-22-12-1-1-12-1-1-12-12-1-1-1-1-1-2-2111111-2-2111111000000220000-1-1-1-10000000-20011
χ1822222-1222222-1-12-1-12-1-1-1-2-2-2-22-12-1-1-12-1-1-12-12-1-1-1-1-1-2-2111111-2-2111111000000-2-2000011110000000200-1-1
χ1922222-1-2-2-2-222-1-12-1-12-1-1-12i2i−2i−2i-21-2111-2111-212-111-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii00000000000033−3−30000000000−i3i3
χ2022222-1-2-2-2-222-1-12-1-12-1-1-12i2i−2i−2i-21-2111-2111-212-111-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000−3−3330000000000i3−i3
χ2122222-1-2-2-2-222-1-12-1-12-1-1-1−2i−2i2i2i-21-2111-2111-212-111-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000000033−3−30000000000i3−i3
χ2222222-1-2-2-2-222-1-12-1-12-1-1-1−2i−2i2i2i-21-2111-2111-212-111-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i000000000000−3−3330000000000−i3i3
χ232222-122222-1-122-12-12-1-1-12222-12-12-1-1-12-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100002200-1-1-1-1000000000020-1-100
χ242222-122222-1-122-12-12-1-1-12222-12-12-1-1-12-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-20011110000000000-201100
χ252222-122222-1-122-12-12-1-1-1-2-2-2-2-12-12-1-1-12-1-1-12-12-1-1-1-111-2-2111111-2-2111100002200-1-1-1-10000000000-201100
χ262222-122222-1-122-12-12-1-1-1-2-2-2-2-12-12-1-1-12-1-1-12-12-1-1-1-111-2-2111111-2-211110000-2-2001111000000000020-1-100
χ272222-12-2-2-2-2-1-122-12-12-1-1-12i2i−2i−2i1-21-2111-2111-2-1211-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii0000000033−3−3000000000000−i3i300
χ282222-12-2-2-2-2-1-122-12-12-1-1-12i2i−2i−2i1-21-2111-2111-2-1211-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii00000000−3−333000000000000i3−i300
χ292222-12-2-2-2-2-1-122-12-12-1-1-1−2i−2i2i2i1-21-2111-2111-2-1211-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000033−3−3000000000000i3−i300
χ302222-12-2-2-2-2-1-122-12-12-1-1-1−2i−2i2i2i1-21-2111-2111-2-1211-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i00000000−3−333000000000000−i3i300
χ3122-2-222200-22-22-2-2-2202-2-22−22−22200000000-2-2002-2002−22−222−2−22−22−222−2−222−2−2000000000000002-22−2000000
χ3222-2-222200-22-22-2-2-2202-2-22−22−22200000000-2-2002-2002−22−222−2−22−22−222−2−2−2−22200000000000000-22−22000000
χ3322-2-222200-22-22-2-2-2202-2-2−22−222200000000-2-2002-200−22−22−2−222−22−22−2−22222−2−200000000000000-222−2000000
χ3422-2-222200-22-22-2-2-2202-2-2−22−222200000000-2-2002-200−22−22−2−222−22−22−2−222−2−222000000000000002-2−22000000
χ3522-2-222-20022-22-2-2-2202-2-2−i2i2i2−i2-2-2000000002200-2200−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i222−2−20000000000002i−2i00−22000000
χ3622-2-222-20022-22-2-2-2202-2-2−i2i2i2−i2-2-2000000002200-2200−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i2−2−222000000000000−2i2i002−2000000
χ3722-2-222-20022-22-2-2-2202-2-2i2−i2−i2i2-2-2000000002200-2200i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i222−2−2000000000000−2i2i00−22000000
χ3822-2-222-20022-22-2-2-2202-2-2i2−i2−i2i2-2-2000000002200-2200i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2−2−2220000000000002i−2i002−2000000
χ392-2-222202-20-2-2-2-22220-22-20000002222-2-2-2-20000000000000000000000002-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-2-222202-20-2-2-2-22220-22-20000002222-2-2-2-20000000000000000000000002-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ412-2-222202-20-2-2-2-22220-22-20000002222-2-2-2-2000000000000000000000000-22-22−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ422-2-222202-20-2-2-2-22220-22-20000002222-2-2-2-2000000000000000000000000-22-22i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4344444-24-4-4444-2-24-2-2-4-2-2-200004-2-4222-42224-2-42-2-22200000000000000000000000000000000000000000000
χ4444444-2-444-444-2-24-2-2-4-2-2-20000-424-2-2-24-2-2-2-42-42222200000000000000000000000000000000000000000000
χ454444-244-4-44-2-244-24-2-4-2-2-20000-242-4222-422-242-4-2-22200000000000000000000000000000000000000000000
χ464444-24-444-4-2-244-24-2-4-2-2-200002-4-24-2-2-24-2-22-42-4222200000000000000000000000000000000000000000000
χ474444-2-24444-2-2-2-2-2-2141114444-2-2-2-211-2-211-2-2-2-21111-2-2-2-21111-2-2-2-211110000000000000000000000000000
χ484444-2-24444-2-2-2-2-2-214111-4-4-4-4-2-2-2-211-2-211-2-2-2-211112222-1-1-1-12222-1-1-1-10000000000000000000000000000
χ494444-2-24-4-44-2-2-2-2-2-21-41110000-2-222-1-122-1-1-2-22211-1-100003i−3i3i−3i00003i−3i3i−3i0000000000000000000000000000
χ504444-2-24-4-44-2-2-2-2-2-21-41110000-2-222-1-122-1-1-2-22211-1-10000−3i3i−3i3i0000−3i3i−3i3i0000000000000000000000000000
χ514444-2-2-444-4-2-2-2-2-2-21-4111000022-2-211-2-2112222-1-1-1-100003-33-30000-33-330000000000000000000000000000
χ524444-2-2-444-4-2-2-2-2-2-21-4111000022-2-211-2-2112222-1-1-1-10000-33-3300003-33-30000000000000000000000000000
χ534444-2-2-4-4-4-4-2-2-2-2-2-2141114i4i−4i−4i2222-1-122-1-122-2-2-1-111−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000
χ544444-2-2-4-4-4-4-2-2-2-2-2-214111−4i−4i4i4i2222-1-122-1-122-2-2-1-1112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000
χ5544-4-44-2400-44-4-22-42-20-22222−2222−224-200000000-4200-220022−22−22−2−22222−22−22−2−2220000000000000000000000000000
χ5644-4-44-2400-44-4-22-42-20-222−2222−22224-200000000-4200-2200−22222−222−2−2−22222−222−2−20000000000000000000000000000
χ5744-4-44-2-40044-4-22-42-20-222−2i22i22i2−2i2-42000000004-2002-200−2i22i2i2−i2i2i2−i2−i22i2−2i2−i2i2−i2−i2i2i20000000000000000000000000000
χ5844-4-44-2-40044-4-22-42-20-2222i2−2i2−2i22i2-42000000004-2002-2002i2−2i2−i2i2−i2−i2i2i2−2i22i2i2−i2i2i2−i2−i20000000000000000000000000000
χ5944-4-4-24400-4-224-42-4-20-22222−2222−22-24000000002-400-2200−2222−22−2−222−2222−22−2−2220000000000000000000000000000
χ6044-4-4-24400-4-224-42-4-20-222−2222−2222-24000000002-400-22002−2−222222−2−22−2−222222−2−20000000000000000000000000000
χ6144-4-4-24-4004-224-42-4-20-222−2i22i22i2−2i22-400000000-24002-200i2−i2−2i22i2i2i2−i2−i2−i2i22i2−2i2−i2−i2i2i20000000000000000000000000000
χ6244-4-4-24-4004-224-42-4-20-2222i2−2i2−2i22i22-400000000-24002-200−i2i22i2−2i2−i2−i2i2i2i2−i2−2i22i2i2i2−i2−i20000000000000000000000000000
χ6344-4-4-2-2400-4-22-2222101-1-122−2222−22-2-2003i−3i003i−3i22001-13i−3i−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−ζ13−2ζ230000000000000000000000000000
χ6444-4-4-2-2400-4-22-2222101-1-122−2222−22-2-200−3i3i00−3i3i22001-1−3i3i−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+ζ230000000000000000000000000000
χ6544-4-4-2-2400-4-22-2222101-1-1−2222−2222-2-2003i−3i003i−3i22001-13i−3i2−22−22ζ5+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+2ζ230000000000000000000000000000
χ6644-4-4-2-2400-4-22-2222101-1-1−2222−2222-2-200−3i3i00−3i3i22001-1−3i3i2−22−2−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−ζ230000000000000000000000000000
χ6744-4-4-2-2-4004-22-2222101-1-1−2i22i22i2−2i222003i−3i003i−3i-2-200-11−3i3ii2−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+ζ13−2ζ230000000000000000000000000000
χ6844-4-4-2-2-4004-22-2222101-1-1−2i22i22i2−2i22200−3i3i00−3i3i-2-200-113i−3ii2−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+ζ230000000000000000000000000000
χ6944-4-4-2-2-4004-22-2222101-1-12i2−2i2−2i22i222003i−3i003i−3i-2-200-11−3i3i−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+2ζ230000000000000000000000000000
χ7044-4-4-2-2-4004-22-2222101-1-12i2−2i2−2i22i22200−3i3i00−3i3i-2-200-113i−3i−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−ζ230000000000000000000000000000
χ714-44-4440000-44-44-4-440-4-440000000000000000000000000000000000000022−22−2222000000000000000000000000
χ724-44-4440000-44-44-4-440-4-4400000000000000000000000000000000000000−222222−22000000000000000000000000
χ734-4-44440-440-4-4-4-44440-44-4000000-4-4-4-444440000000000000000000000000000000000000000000000000000
χ744-4-444-204-40-4-4224-2-202-220000004-2-2-2-4222000000000000000000000000000000−2i22i20000i2−i2i2−i2000000000000
χ754-4-444-204-40-4-4224-2-202-220000004-2-2-2-42220000000000000000000000000000002i2−2i20000−i2i2−i2i2000000000000
χ764-4-444-20-440-4-4224-2-202-22000000-42224-2-2-2000000000000000000000000000000000000i6−i6−i6i6000000000000
χ774-4-444-20-440-4-4224-2-202-22000000-42224-2-2-2000000000000000000000000000000000000−i6i6i6−i6000000000000
χ784-4-44-2404-4022-4-4-24-202-22000000-24-2-22-4220000000000000000000000000000−2i22i200i2−i2i2−i20000000000000000
χ794-4-44-2404-4022-4-4-24-202-22000000-24-2-22-42200000000000000000000000000002i2−2i200−i2i2−i2i20000000000000000
χ804-4-44-240-44022-4-4-24-202-220000002-422-24-2-200000000000000000000000000000000i6−i6−i6i60000000000000000
χ814-4-44-240-44022-4-4-24-202-220000002-422-24-2-200000000000000000000000000000000−i6i6i6−i60000000000000000
χ828-88-88-40000-884-4-84-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ838-88-8-4800004-4-884-8-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-4-400004-44-44420-2-22000000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000
χ858-88-8-4-400004-44-44420-2-2200000000−6i6i006i−6i0000000000000000000000000000000000000000000000000000
χ868-8-88-4-408-804444-4-420-22-2000000-4-42244-2-20000000000000000000000000000000000000000000000000000
χ878-8-88-4-40-8804444-4-420-22-200000044-2-2-4-4220000000000000000000000000000000000000000000000000000

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