Finite Group Databasebeta

← Group #11723344

Character table — Group #11723344

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222222222244444444444444444444444444444444444444444444444412122424242424242424363654547272108
order123333346666633336666812121212121212121212121212242424242424242424242424242424242424242424242424242424666612121212442412128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11
χ5111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-1111-1-1
χ6111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-11-1-1-111
χ7111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-11-11
χ8111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1111-11-1
χ92222222-222222222222220-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000002-2000
χ102222222-222222222222220-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000-22000
χ112222-1-1-122-1-1-122-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-12-1-1-10000000
χ122222-1-1-122-1-1-122-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111-21110000000
χ132222-1-1-122-1-1-122-1-1-12-1-1-1-22-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111112-22-1-1-1-21110000000
χ142222-1-1-122-1-1-122-1-1-12-1-1-1-22-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111-22-21112-1-1-10000000
χ15222-12-1-12-12-1-12-12-1-1-12-1-12-12-1-12-1-122-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-12-1-1-12-1-10000000
χ16222-12-1-12-12-1-12-12-1-1-12-1-12-12-1-12-1-122-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-21-2111-2110000000
χ17222-12-1-12-12-1-12-12-1-1-12-1-1-2-12-1-12-1-122-1-1-1-1-2-2111111-2-2-2-2-2-21111111111112-2-12-1-11-2110000000
χ18222-12-1-12-12-1-12-12-1-1-12-1-1-2-12-1-12-1-122-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111-221-211-12-1-10000000
χ19222-1-12-12-1-12-12-1-12-1-1-12-12-1-12-12-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-122-1-12-1-1-12-10000000
χ20222-1-12-12-1-12-12-1-12-1-1-12-12-1-12-12-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-2-211-2111-210000000
χ21222-1-12-12-1-12-12-1-12-1-1-12-1-2-1-12-12-1-1-1-122-1-1-2-2111111111111-2-2-2-2-2-21111112-2-1-12-111-210000000
χ22222-1-12-12-1-12-12-1-12-1-1-12-1-2-1-12-12-1-1-1-122-1-1-2-2111111111111-2-2-2-2-2-2111111-2211-21-1-12-10000000
χ23222-1-1-122-1-1-122-1-1-12-1-1-122-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-12-1-1-120000000
χ24222-1-1-122-1-1-122-1-1-12-1-1-122-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2111-2111-20000000
χ25222-1-1-122-1-1-122-1-1-12-1-1-12-2-1-1-122-1-1-1-1-1-122-2-2111111111111111111-2-2-2-2-2-22-2-1-1-12111-20000000
χ26222-1-1-122-1-1-122-1-1-12-1-1-12-2-1-1-122-1-1-1-1-1-122-2-2111111111111111111-2-2-2-2-2-2-22111-2-1-1-120000000
χ2722-1222222222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-100000000002200-1-10
χ2822-1222222222-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-10000000000-2-200110
χ2922-1222222222-1-1-1-1-1-1-1-1-1-22222-1-1-1-1-1-1-1-1-111-2-21111-2-21111-2-21111-2-2111100000000002-200-110
χ3022-1222222222-1-1-1-1-1-1-1-1-1-22222-1-1-1-1-1-1-1-1-111-2-21111-2-21111-2-21111-2-211110000000000-22001-10
χ314444-2-2-2-44-2-2-244-2-2-24-2-2-20-4222-4-4-42222220000000000000000000000000000000000000000000
χ32444-24-2-2-4-24-2-24-24-2-2-24-2-202-422-422-4-422220000000000000000000000000000000000000000000
χ33444-2-24-2-4-2-24-24-2-24-2-2-24-2022-42-42222-4-4220000000000000000000000000000000000000000000
χ34444-2-2-24-4-2-2-244-2-2-24-2-2-240222-4-4222222-4-40000000000000000000000000000000000000000000
χ3544-24444-44444-2-2-2-2-2-2-2-2-20-4-4-4-42222222220000000000000000000000000000000000000000000
χ3644-24-2-2-244-2-2-2-2-2111-211144-2-2-2-2-2-2111111-2-244-2-2-2-2-2-21111-2-21111-2-2111100000000000000000
χ3744-24-2-2-244-2-2-2-2-2111-2111-44-2-2-2-2-2-211111122-4-4222222-1-1-1-122-1-1-1-122-1-1-1-100000000000000000
χ3844-24-2-2-2-44-2-2-2-2-2111-21110-4222222-1-1-1-1-1-100000000003i3i−3i−3i003i3i−3i−3i003i3i−3i−3i00000000000000000
χ3944-24-2-2-2-44-2-2-2-2-2111-21110-4222222-1-1-1-1-1-10000000000−3i−3i3i3i00−3i−3i3i3i00−3i−3i3i3i00000000000000000
χ4044-2-24-2-24-24-2-2-21-2111-2114-24-2-2-211-2-21111-2-2-2-2111144-2-2-2-2-2-21111-2-2111100000000000000000
χ4144-2-24-2-24-24-2-2-21-2111-211-4-24-2-2-211-2-211112222-1-1-1-1-4-4222222-1-1-1-122-1-1-1-100000000000000000
χ4244-2-24-2-2-4-24-2-2-21-2111-21102-4222-1-122-1-1-1-100003i3i−3i−3i000000003i3i−3i−3i00−3i−3i3i3i00000000000000000
χ4344-2-24-2-2-4-24-2-2-21-2111-21102-4222-1-122-1-1-1-10000−3i−3i3i3i00000000−3i−3i3i3i003i3i−3i−3i00000000000000000
χ4444-2-2-24-24-2-24-2-211-2111-214-2-24-2-21111-2-211-2-2-2-21111-2-2111144-2-2-2-2-2-2111100000000000000000
χ4544-2-2-24-24-2-24-2-211-2111-21-4-2-24-2-21111-2-2112222-1-1-1-122-1-1-1-1-4-4222222-1-1-1-100000000000000000
χ4644-2-2-24-2-4-2-24-2-211-2111-21022-422-1-1-1-122-1-100003i3i−3i−3i00−3i−3i3i3i000000003i3i−3i−3i00000000000000000
χ4744-2-2-24-2-4-2-24-2-211-2111-21022-422-1-1-1-122-1-10000−3i−3i3i3i003i3i−3i−3i00000000−3i−3i3i3i00000000000000000
χ4844-2-2-2-244-2-2-24-2111-2111-24-2-2-24-2111111-2-2-2-2-2-21111-2-21111-2-2111144-2-2-2-200000000000000000
χ4944-2-2-2-244-2-2-24-2111-2111-2-4-2-2-24-2111111-2-22222-1-1-1-122-1-1-1-122-1-1-1-1-4-4222200000000000000000
χ5044-2-2-2-24-4-2-2-24-2111-2111-20222-42-1-1-1-1-1-12200003i3i−3i−3i003i3i−3i−3i00−3i−3i3i3i00000000000000000000000
χ5144-2-2-2-24-4-2-2-24-2111-2111-20222-42-1-1-1-1-1-1220000−3i−3i3i3i00−3i−3i3i3i003i3i−3i−3i00000000000000000000000
χ524-4444440-4-4-4-4-44444-4-4-4-4000000000000000000000000000000000000000000000000000000000
χ534-444-2-2-20-4222-44-2-2-2-422200000000000000000000006−66−66−66−66−66−66−66−66−600000000000000000
χ544-444-2-2-20-4222-44-2-2-2-42220000000000000000000000−66−66−66−66−66−66−66−66−6600000000000000000
χ554-44-24-2-202-422-4-24-2-22-42200000000000000006−66−66−60000006−66−66−6−66−66−6600000000000000000
χ564-44-24-2-202-422-4-24-2-22-4220000000000000000−66−66−66000000−66−66−666−66−66−600000000000000000
χ574-44-2-24-2022-42-4-2-24-222-4200000000000000006−66−66−6−66−66−660000006−66−66−600000000000000000
χ584-44-2-24-2022-42-4-2-24-222-420000000000000000−66−66−666−66−66−6000000−66−66−6600000000000000000
χ594-44-2-2-240222-4-4-2-2-24222-400000000000000006−66−66−66−66−66−6−66−66−6600000000000000000000000
χ604-44-2-2-240222-4-4-2-2-24222-40000000000000000−66−66−66−66−66−666−66−66−600000000000000000000000
χ614-4-244440-4-4-4-42-2-2-2-2222200000000000000i6−i600i6−i6−i6i600i6−i6−i6i600i6−i6−i6i600i6−i6−i6i600000000000000000
χ624-4-244440-4-4-4-42-2-2-2-2222200000000000000−i6i600−i6i6i6−i600−i6i6i6−i600−i6i6i6−i600−i6i6i6−i600000000000000000
χ634-4-24-2-2-20-42222-21112-1-1-1000000003i−3i3i−3i3i−3ii6−i600i6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000
χ644-4-24-2-2-20-42222-21112-1-1-1000000003i−3i3i−3i3i−3i−i6i600−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000
χ654-4-24-2-2-20-42222-21112-1-1-100000000−3i3i−3i3i−3i3ii6−i600i6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000
χ664-4-24-2-2-20-42222-21112-1-1-100000000−3i3i−3i3i−3i3i−i6i600−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000
χ674-4-2-24-2-202-42221-211-12-1-10000003i−3i003i−3i−3i3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300i6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000
χ684-4-2-24-2-202-42221-211-12-1-10000003i−3i003i−3i−3i3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000
χ694-4-2-24-2-202-42221-211-12-1-1000000−3i3i00−3i3i3i−3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300i6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000
χ704-4-2-24-2-202-42221-211-12-1-1000000−3i3i00−3i3i3i−3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000
χ714-4-2-2-24-2022-42211-21-1-12-10000003i−3i−3i3i003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300i6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000
χ724-4-2-2-24-2022-42211-21-1-12-10000003i−3i−3i3i003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000
χ734-4-2-2-24-2022-42211-21-1-12-1000000−3i3i3i−3i00−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300i6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000
χ744-4-2-2-24-2022-42211-21-1-12-1000000−3i3i3i−3i00−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000
χ754-4-2-2-2-240222-42111-2-1-1-120000003i−3i3i−3i−3i3i00i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300i6−i6−i6i600000000000000000
χ764-4-2-2-2-240222-42111-2-1-1-120000003i−3i3i−3i−3i3i00−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300−i6i6i6−i600000000000000000
χ774-4-2-2-2-240222-42111-2-1-1-12000000−3i3i−3i3i3i−3i00i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300i6−i6−i6i600000000000000000
χ784-4-2-2-2-240222-42111-2-1-1-12000000−3i3i−3i3i3i−3i00−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300−i6i6i6−i600000000000000000

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