Finite Group Databasebeta

← Group #11781499

Character table — Group #11781499

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222444444444444444444444888888888888888888888818181818242424242424242424242424363636363636484848484848
order12223344446666663466688881212121212121212121212121212121212122424242424242424242424242424242488888888242424242424242444448824661212
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
χ92222222-2-222222222-222200002-2-22-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000022-2-200000000
χ102222222-2-222222222-222200002-2-22-2-2-2-2-2-222-2-222-2-200000000000000000000000000000000-2-22200000000
χ11222222-222-22222222-22220000-222-2222222-2-2-2-2-2-2-2-2000000000000000022220000000000000000-2-2000000
χ12222222-222-22222222-22220000-222-2222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2000000000000000022000000
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
χ1522222-1222222-1-1-12-12-1-1-12222-12-12-1-12-1-1-1-122-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100002200-1-1-1-1000000000020-1-100
χ1622222-1222222-1-1-12-12-1-1-12222-12-12-1-12-1-1-1-122-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-20011110000000000-201100
χ1722222-1222222-1-1-12-12-1-1-1-2-2-2-2-12-12-1-12-1-1-1-122-1-1-1-1-1-2-2111111-2-211111100002200-1-1-1-10000000000-201100
χ1822222-1222222-1-1-12-12-1-1-1-2-2-2-2-12-12-1-12-1-1-1-122-1-1-1-1-1-2-2111111-2-21111110000-2-2001111000000000020-1-100
χ1922222-1-2-2-2-222-1-1-12-12-1-1-12i2i−2i−2i1-21-211-21111-22-111-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii0000000033−3−3000000000000−i3i300
χ2022222-1-2-2-2-222-1-1-12-12-1-1-12i2i−2i−2i1-21-211-21111-22-111-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii00000000−3−333000000000000i3−i300
χ2122222-1-2-2-2-222-1-1-12-12-1-1-1−2i−2i2i2i1-21-211-21111-22-111-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000033−3−3000000000000i3−i300
χ2222222-1-2-2-2-222-1-1-12-12-1-1-1−2i−2i2i2i1-21-211-21111-22-111-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000−3−333000000000000−i3i300
χ232222-122222-1-1222-1-12-1-1-122222-12-1-1-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000220000-1-1-1-10000000200-1-1
χ242222-122222-1-1222-1-12-1-1-122222-12-1-1-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000-2-2000011110000000-20011
χ252222-122222-1-1222-1-12-1-1-1-2-2-2-22-12-1-1-1-12-1-12-1-12-1-1-1-111-2-2111111-2-21111000000220000-1-1-1-10000000-20011
χ262222-122222-1-1222-1-12-1-1-1-2-2-2-22-12-1-1-1-12-1-12-1-12-1-1-1-111-2-2111111-2-21111000000-2-2000011110000000200-1-1
χ272222-12-2-2-2-2-1-1222-1-12-1-1-12i2i−2i−2i-21-21111-211-21-1211-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii00000000000033−3−30000000000−i3i3
χ282222-12-2-2-2-2-1-1222-1-12-1-1-12i2i−2i−2i-21-21111-211-21-1211-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000−3−3330000000000i3−i3
χ292222-12-2-2-2-2-1-1222-1-12-1-1-1−2i−2i2i2i-21-21111-211-21-1211-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i00000000000033−3−30000000000i3−i3
χ302222-12-2-2-2-2-1-1222-1-12-1-1-1−2i−2i2i2i-21-21111-211-21-1211-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000−3−3330000000000−i3i3
χ3122-2-2220-2202-22-2-2-2202-2-200000-2-20-2-222220000000000000000000000002i2i−2i−2i2−2−i2i22−22−2−i2i2−i2i2000000000000
χ3222-2-2220-2202-22-2-2-2202-2-200000-2-20-2-222220000000000000000000000002i2i−2i−2i−22i2−i2−22−22i2−i2i2−i2000000000000
χ3322-2-2220-2202-22-2-2-2202-2-200000-2-20-2-22222000000000000000000000000−2i−2i2i2i2−2i2−i22−22−2i2−i2i2−i2000000000000
χ3422-2-2220-2202-22-2-2-2202-2-200000-2-20-2-22222000000000000000000000000−2i−2i2i2i−22−i2i2−22−22−i2i2−i2i2000000000000
χ352-2-2222200-2-2-2-22-2220-22-2−i2i2−i2i22002000000-2-2002-200−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i22−22−20000000000002i−2i002−2000000
χ362-2-2222200-2-2-2-22-2220-22-2−i2i2−i2i22002000000-2-2002-200−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−22−22000000000000−2i2i00−22000000
χ372-2-2222200-2-2-2-22-2220-22-2i2−i2i2−i22002000000-2-2002-200i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i22−22−2000000000000−2i2i002−2000000
χ382-2-2222200-2-2-2-22-2220-22-2i2−i2i2−i22002000000-2-2002-200i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2−22−220000000000002i−2i00−22000000
χ392-2-2222-2002-2-2-22-2220-22-22−2−22-200-20000002200-22002−22−222−2−2−22−22−2−2222−22−2000000000000002-2−22000000
χ402-2-2222-2002-2-2-22-2220-22-22−2−22-200-20000002200-22002−22−222−2−2−22−22−2−222−22−2200000000000000-222−2000000
χ412-2-2222-2002-2-2-22-2220-22-2−222−2-200-20000002200-2200−22−22−2−2222−22−222−2−22−22−200000000000000-22−22000000
χ422-2-2222-2002-2-2-22-2220-22-2−222−2-200-20000002200-2200−22−22−2−2222−22−222−2−2−22−22000000000000002-22−2000000
χ4344444-24-4-4444-2-2-24-2-4-2-2-20000-2-42422-4222-24-42-2-22200000000000000000000000000000000000000000000
χ4444444-2-444-444-2-2-24-2-4-2-2-2000024-2-4-2-24-2-2-22-4-42222200000000000000000000000000000000000000000000
χ454444-244-4-44-2-2444-2-2-4-2-2-2000042-4-2222-4224-22-4-2-22200000000000000000000000000000000000000000000
χ464444-24-444-4-2-2444-2-2-4-2-2-20000-4-242-2-2-24-2-2-422-4222200000000000000000000000000000000000000000000
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
χ494444-2-24-4-44-2-2-2-2-2-21-41110000-222-2-1-122-1-1-2-22211-1-100003i−3i3i−3i00003i−3i3i−3i0000000000000000000000000000
χ504444-2-24-4-44-2-2-2-2-2-21-41110000-222-2-1-122-1-1-2-22211-1-10000−3i3i−3i3i0000−3i3i−3i3i0000000000000000000000000000
χ514444-2-2-444-4-2-2-2-2-2-21-411100002-2-2211-2-2112222-1-1-1-100003-33-30000-33-330000000000000000000000000000
χ524444-2-2-444-4-2-2-2-2-2-21-411100002-2-2211-2-2112222-1-1-1-10000-33-3300003-33-30000000000000000000000000000
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
χ5544-4-44404-404-44-4-4-4404-4-40000044044-4-4-4-40000000000000000000000000000000000000000000000000000
χ5644-4-44-204-404-4-222-4-20-222000004-20-2-2-4222000000000000000000000000000000006−6−660000000000000000
χ5744-4-44-204-404-4-222-4-20-222000004-20-2-2-422200000000000000000000000000000000−666−60000000000000000
χ5844-4-44-20-4404-4-222-4-20-22200000-420224-2-2-2000000000000000000000000000022−2200−22−220000000000000000
χ5944-4-44-20-4404-4-222-4-20-22200000-420224-2-2-20000000000000000000000000000−2222002−22−20000000000000000
χ6044-4-4-2404-40-224-4-42-20-22200000-240-2-22-422000000000000000000000000000000000000i6−i6−i6i6000000000000
χ6144-4-4-2404-40-224-4-42-20-22200000-240-2-22-422000000000000000000000000000000000000−i6i6i6−i6000000000000
χ6244-4-4-240-440-224-4-42-20-222000002-4022-24-2-2000000000000000000000000000000−2i22i20000i2−i2i2−i2000000000000
χ6344-4-4-240-440-224-4-42-20-222000002-4022-24-2-20000000000000000000000000000002i2−2i20000−i2i2−i2i2000000000000
χ644-44-4440000-44-4-44-440-4-4400000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ654-44-4440000-44-4-44-440-4-44000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ664-4-444-2400-4-4-42-224-202-22−2i22i2−2i22i2-20040000002-400-2200−2i22i2i2−i2i2i2−i2−i2−2i22i2i2−i2i2i2−i2−i20000000000000000000000000000
χ674-4-444-2400-4-4-42-224-202-222i2−2i22i2−2i2-20040000002-400-22002i2−2i2−i2i2−i2−i2i2i22i2−2i2−i2i2−i2−i2i2i20000000000000000000000000000
χ684-4-444-2-4004-4-42-224-202-2222−22−2222200-4000000-24002-20022−22−22−2−222−22222−222−2−20000000000000000000000000000
χ694-4-444-2-4004-4-42-224-202-22−222222−22200-4000000-24002-200−22222−222−2−222−22−22−2−2220000000000000000000000000000
χ704-4-44-24400-422-44-4-2-202-22−2i22i2−2i22i2400-2000000-4200-2200i2−i2−2i22i2i2i2−i2−i2i2−i2−2i22i2i2i2−i2−i20000000000000000000000000000
χ714-4-44-24400-422-44-4-2-202-222i2−2i22i2−2i2400-2000000-4200-2200−i2i22i2−2i2−i2−i2i2i2−i2i22i2−2i2−i2−i2i2i20000000000000000000000000000
χ724-4-44-24-400422-44-4-2-202-2222−22−2222-40020000004-2002-200−2222−22−2−2222−2−222222−2−20000000000000000000000000000
χ734-4-44-24-400422-44-4-2-202-22−222222−22-40020000004-2002-2002−2−222222−2−2−2222−22−2−2220000000000000000000000000000
χ744-4-44-2-2400-4222-22-210-11-1−2i22i2−2i22i2-200-23i−3i003i−3i22001-13i−3ii2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ230000000000000000000000000000
χ754-4-44-2-2400-4222-22-210-11-1−2i22i2−2i22i2-200-2−3i3i00−3i3i22001-1−3i3ii2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ230000000000000000000000000000
χ764-4-44-2-2400-4222-22-210-11-12i2−2i22i2−2i2-200-23i−3i003i−3i22001-13i−3i−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ230000000000000000000000000000
χ774-4-44-2-2400-4222-22-210-11-12i2−2i22i2−2i2-200-2−3i3i00−3i3i22001-1−3i3i−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ230000000000000000000000000000
χ784-4-44-2-2-4004222-22-210-11-122−22−222220023i−3i003i−3i-2-200-11−3i3i−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ232−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ230000000000000000000000000000
χ794-4-44-2-2-4004222-22-210-11-122−22−22222002−3i3i00−3i3i-2-200-113i−3i−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ230000000000000000000000000000
χ804-4-44-2-2-4004222-22-210-11-1−222222−2220023i−3i003i−3i-2-200-11−3i3i2−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ230000000000000000000000000000
χ814-4-44-2-2-4004222-22-210-11-1−222222−222002−3i3i00−3i3i-2-200-113i−3i2−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ230000000000000000000000000000
χ8288-8-8-4-408-80-44-4444202-2-200000-4-402244-2-20000000000000000000000000000000000000000000000000000
χ8388-8-8-4-40-880-44-4444202-2-200000440-2-2-4-4220000000000000000000000000000000000000000000000000000
χ848-88-88-40000-8844-4-8-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ858-88-8-4800004-4-8-884-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8-4-400004-444-4420-2-22000000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000
χ878-88-8-4-400004-444-4420-2-2200000000−6i6i006i−6i0000000000000000000000000000000000000000000000000000

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