Finite Group Databasebeta

← Group #11781748

Character table — Group #11781748

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222244444444444444444888888888888888888888888242424242424242424242424363636364848484848487272
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242444881212121224242424888822666688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-11-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-11111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-111-1-111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ92222222-2-222222222-22222-2-2-22222222-200-2-2-2-2-2-200000000000000002-20022-2-20000000000000000
χ102222222-2-222222222-22222-2-2-22222222-200-2-2-2-2-2-20000000000000000-2200-2-2220000000000000000
χ11222222-222-22222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000022-2-200000000
χ12222222-222-22222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000-2-22200000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2220000000000000000002i−2i00002i2i−2i−2i000000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000−2i2i0000−2i−2i2i2i000000000000
χ1522222-12222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12200-1-1-1-10000000020-1-10000
χ1622222-12222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200111100000000-20110000
χ1722222-12222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-21111111111112200-1-1-1-100000000-20110000
χ1822222-12222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-2111111111111-2-20011110000000020-1-10000
χ1922222-12-2-22222-1-1-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32-200-1-1110000000000−i3i30000
χ2022222-12-2-22222-1-1-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-220011-1-10000000000i3−i30000
χ2122222-12-2-22222-1-1-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32-200-1-1110000000000i3−i30000
χ2222222-12-2-22222-1-1-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-220011-1-10000000000−i3i30000
χ232222-122222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100220000-1-1-1-100000200-1-100
χ242222-122222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100-2-20000111100000-2001100
χ252222-122222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-2111100220000-1-1-1-100000-2001100
χ262222-122222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-2111100-2-20000111100000200-1-100
χ272222-12-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-133−3−30033−3−30033−3−3002i−2i0000−i−iii00000000−i3i300
χ282222-12-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-133−3−30033−3−30033−3−300−2i2i0000ii−i−i00000000i3−i300
χ292222-12-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-1−3−33300−3−33300−3−333002i−2i0000−i−iii00000000i3−i300
χ302222-12-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-1−3−33300−3−33300−3−33300−2i2i0000ii−i−i00000000−i3i300
χ3122-2-22202-202-2-22-2-2202-2-2022-20000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000002-200000000−i2i2
χ3222-2-22202-202-2-22-2-2202-2-2022-20000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000-2200000000i2−i2
χ3322-2-22202-202-2-22-2-2202-2-2022-20000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000002-200000000i2−i2
χ3422-2-22202-202-2-22-2-2202-2-2022-20000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000-2200000000−i2i2
χ3544444-2-444-4444-2-2-2-2-4-2-2-2-44-2-2222-4222400-42-2-2220000000000000000000000000000000000000000
χ3644444-2-4-4-4-4444-2-2-2-24-2-2-2-4-422222-4222-4004-222-2-20000000000000000000000000000000000000000
χ374444-244-4-44-2-2-2444-2-4-2-2-2-22-4-44-2-2-24-2-22002-422220000000000000000000000000000000000000000
χ384444-24-444-4-2-2-2444-2-4-2-2-22-244-4222-422-2002-4-2-2220000000000000000000000000000000000000000
χ394444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000
χ404444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000
χ414444-2-24-4-44-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000
χ424444-2-24-4-44-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000
χ434444-2-2-444-4-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000
χ444444-2-2-444-4-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000
χ454444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1112323−23−2300−3−33300−3−333000000000000000000000000
χ464444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-111−23−2323230033−3−30033−3−3000000000000000000000000
χ4744-4-4440-4404-4-44-4-4404-4-40-4-44000000040000-44000000000000000000000000000000000000000000
χ4844-4-44-204-404-4-4-222-20-22204-220000000-4−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ4944-4-44-204-404-4-4-222-20-22204-220000000-42i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ5044-4-44-20-4404-4-4-222-20-2220-42-20000000400002-20000006−66−66−6−66−66−66000000000000000000000000
χ5144-4-44-20-4404-4-4-222-20-2220-42-20000000400002-2000000−66−66−666−66−66−6000000000000000000000000
χ5244-4-4-2404-40-2224-4-4-20-2220-24-400000002−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000
χ5344-4-4-2404-40-2224-4-4-20-2220-24-4000000022i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000
χ5444-4-4-240-440-2224-4-4-20-22202-440000000-200002-200i6−i6−i6i600i6−i6−i6i600i6−i6−i6i6000000000000000000000000
χ5544-4-4-240-440-2224-4-4-20-22202-440000000-200002-200−i6i6i6−i600−i6i6i6−i600−i6i6i6−i6000000000000000000000000
χ5644-4-4-2-204-40-222-222101-1-10-2-2203i−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−ζ23000000000000000000000000
χ5744-4-4-2-204-40-222-222101-1-10-2-2203i−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+ζ23000000000000000000000000
χ5844-4-4-2-204-40-222-222101-1-10-2-220−3i3i00−3i3i2−2i22i2001-1−3i3ii2−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+2ζ23000000000000000000000000
χ5944-4-4-2-204-40-222-222101-1-10-2-220−3i3i00−3i3i22i2−2i2001-1−3i3i−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+ζ13−2ζ23000000000000000000000000
χ6044-4-4-2-20-440-222-222101-1-1022-203i−3i003i−3i-20000-11−3i3ii6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ6144-4-4-2-20-440-222-222101-1-1022-203i−3i003i−3i-20000-11−3i3i−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ6244-4-4-2-20-440-222-222101-1-1022-20−3i3i00−3i3i-20000-113i−3ii6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ6344-4-4-2-20-440-222-222101-1-1022-20−3i3i00−3i3i-20000-113i−3i−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ644-44-4440000-44-4-44-440-44-40000000000000000000000000000000000000000000000000022−2200000000
χ654-44-4440000-44-4-44-440-44-400000000000000000000000000000000000000000000000000−222200000000
χ664-4-4444400-4-4-44-4-4440-4-44-4000-4-4-444440000000000000000000000000000000000000000000000000
χ674-4-4444-4004-4-44-4-4440-4-444000444-4-4-4-40000000000000000000000000000000000000000000000000
χ684-4-444-2400-4-4-4422-2-2022-2-40002224-2-2-20000000000000000000000000000000−2i32i30000000000000000
χ694-4-444-2400-4-4-4422-2-2022-2-40002224-2-2-200000000000000000000000000000002i3−2i30000000000000000
χ704-4-444-2-4004-4-4422-2-2022-24000-2-2-2-42220000000000000000000000000000023−23000000000000000000
χ714-4-444-2-4004-4-4422-2-2022-24000-2-2-2-422200000000000000000000000000000−2323000000000000000000
χ724-4-44-24400-422-2-4-44-2022-22000-422-24-2-2000000000000000000000000000000000i6−i6i6−i6000000000000
χ734-4-44-24400-422-2-4-44-2022-22000-422-24-2-2000000000000000000000000000000000−i6i6−i6i6000000000000
χ744-4-44-24-400422-2-4-44-2022-2-20004-2-22-4220000000000000000000000000000000006−6−66000000000000
χ754-4-44-24-400422-2-4-44-2022-2-20004-2-22-422000000000000000000000000000000000−666−6000000000000
χ768-88-88-40000-88-84-44-404-44000000000000000000000000000000000000000000000000000000000000
χ778-88-8-4800004-44-88-8-404-44000000000000000000000000000000000000000000000000000000000000
χ788-88-8-4-400004-444-4420-22-2000006i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ798-88-8-4-400004-444-4420-22-200000−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ808-8-88-4-4800-844-444-420-2-2240004-2-2-4-4220000000000000000000000000000000000000000000000000
χ818-8-88-4-4-800844-444-420-2-22-4000-42244-2-20000000000000000000000000000000000000000000000000

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