Finite Group Databasebeta

← Group #13149811

Character table — Group #13149811

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size112222244466661212121212121212121212121212181836363636363636363672727272112222244466661212121212121212121212121212181836363636363636363672727272
order123461212824243366361212121224242424242424242422246812242466612226461212824246666661212121224242424242424242422246812242466612
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111111111111111111111111-1-1-1-111111-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-1-11-1-111111111111111111111111111111-1-1-1-111-1-1-1-1-11-1-11
χ51111111-1-1-11111111111-1-1-1-1-1-1-1-1111-11-11-11-1-111-1-11111111-1-1-11111111111-1-1-1-1-1-1-1-1111-11-11-11-1-111-1-1
χ61111111-1-1-11111111111-1-1-1-1-1-1-1-111-11-111-11-1-1-1-1111111111-1-1-11111111111-1-1-1-1-1-1-1-111-11-111-11-1-1-1-111
χ71111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-11-111-11-111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-11-111-11-11
χ81111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-11-1111-11-11111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-11-1111-11-1
χ922222222222-1-12-1-1-12-1-122-1-1-1-1-1-1002200000000-1-1022222222222-1-12-1-1-12-1-122-1-1-1-1-1-1002200000000-1-10
χ1022222222222-1-12-1-1-12-1-122-1-1-1-1-1-100-2-20000000011022222222222-1-12-1-1-12-1-122-1-1-1-1-1-100-2-200000000110
χ112222222222-122-1-1-12-1-1-1-1-122-1-1-1-100002200000-100-12222222222-122-1-1-12-1-1-1-1-122-1-1-1-100002200000-100-1
χ122222222222-122-1-1-12-1-1-1-1-122-1-1-1-10000-2-20000010012222222222-122-1-1-12-1-1-1-1-122-1-1-1-10000-2-2000001001
χ132222222-2-2-22-1-12-1-1-12-1-1-2-2111111002-200000000-1102222222-2-2-22-1-12-1-1-12-1-1-2-2111111002-200000000-110
χ142222222-2-2-22-1-12-1-1-12-1-1-2-211111100-22000000001-102222222-2-2-22-1-12-1-1-12-1-1-2-211111100-22000000001-10
χ152222222-2-2-2-122-1-1-12-1-1-111-2-2111100002-200000-10012222222-2-2-2-122-1-1-12-1-1-111-2-2111100002-200000-1001
χ162222222-2-2-2-122-1-1-12-1-1-111-2-211110000-2200000100-12222222-2-2-2-122-1-1-12-1-1-111-2-211110000-2200000100-1
χ17222-22-2-2000222222-2-2-2-2000000002-2000020-2000000222-22-2-2000222222-2-2-2-2000000002-2000020-2000000
χ18222-22-2-2000222222-2-2-2-200000000-220000-202000000222-22-2-2000222222-2-2-2-200000000-220000-202000000
χ194444444444-2-2-2-211-2-211-2-2-2-211110000000000000004444444444-2-2-2-211-2-211-2-2-2-21111000000000000000
χ204444444-4-4-4-2-2-2-211-2-2112222-1-1-1-10000000000000004444444-4-4-4-2-2-2-211-2-2112222-1-1-1-1000000000000000
χ21444-44-4-40004-2-24-2-22-42200000000000000000000000444-44-4-40004-2-24-2-22-42200000000000000000000000
χ22444-44-4-4000-244-2-2-2-422200000000000000000000000444-44-4-4000-244-2-2-2-422200000000000000000000000
χ23444-44-4-4000-2-2-2-21122-1-100003i3i−3i−3i000000000000000444-44-4-4000-2-2-2-21122-1-100003i3i−3i−3i000000000000000
χ24444-44-4-4000-2-2-2-21122-1-10000−3i−3i3i3i000000000000000444-44-4-4000-2-2-2-21122-1-10000−3i−3i3i3i000000000000000
χ254-440-40000044-4-44-40000000000000000000000000004-440-40000044-4-44-4000000000000000000000000000
χ264-440-4000004-22-4-22000000i6−i6i6−i6i6−i60000000000000004-440-4000004-22-4-22000000i6−i6i6−i6i6−i6000000000000000
χ274-440-4000004-22-4-22000000−i6i6−i6i6−i6i60000000000000004-440-4000004-22-4-22000000−i6i6−i6i6−i6i6000000000000000
χ284-440-400000-24-42-2200006−6006−6−660000000000000004-440-400000-24-42-2200006−6006−6−66000000000000000
χ294-440-400000-24-42-220000−6600−666−60000000000000004-440-400000-24-42-220000−6600−666−6000000000000000
χ304-440-400000-2-2221-1003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000004-440-400000-2-2221-1003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000
χ314-440-400000-2-2221-1003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000004-440-400000-2-2221-1003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000
χ324-440-400000-2-2221-100−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000004-440-400000-2-2221-100−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000
χ334-440-400000-2-2221-100−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000004-440-400000-2-2221-100−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000
χ3466-36-3-3-36-3-3000000000000000000220000-12-1-1-1000066-36-3-3-36-3-3000000000000000000220000-12-1-1-10000
χ3566-36-3-3-36-3-3000000000000000000-2-200001-2111000066-36-3-3-36-3-3000000000000000000-2-200001-21110000
χ3666-36-3-3-3-633000000000000000000220000-1-2-111000066-36-3-3-3-633000000000000000000220000-1-2-1110000
χ3766-36-3-3-3-633000000000000000000-2-20000121-1-1000066-36-3-3-3-633000000000000000000-2-20000121-1-10000
χ3866-3-6-333033−330000000000000000002-20000-1013−3000066-3-6-333033−330000000000000000002-20000-1013−30000
χ3966-3-6-333033−33000000000000000000-22000010-1−33000066-3-6-333033−33000000000000000000-22000010-1−330000
χ4066-3-6-3330−33330000000000000000002-20000-101−33000066-3-6-3330−33330000000000000000002-20000-101−330000
χ4166-3-6-3330−3333000000000000000000-22000010-13−3000066-3-6-3330−3333000000000000000000-22000010-13−30000
χ4212-12-60663−6300000000000000000000000000000000000012-12-60663−63000000000000000000000000000000000000
χ4312-12-606−636300000000000000000000000000000000000012-12-606−6363000000000000000000000000000000000000
χ441111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ45111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111
χ461111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11
χ471111111111111111111111111111-1-1-1-111-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-111-1
χ481111111-1-1-11111111111-1-1-1-1-1-1-1-1111-11-11-11-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-11-11-111-1-111
χ491111111-1-1-11111111111-1-1-1-1-1-1-1-111-11-111-11-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-11-11-1-11-11111-1-1
χ501111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-11-111-11-11-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111111-111-11-11-1-11-11-1
χ511111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-11-1111-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111111-1-111-11-1-1-11-11
χ5222222222222-1-12-1-1-12-1-122-1-1-1-1-1-1002200000000-1-10-2-2-2-2-2-2-2-2-2-2-211-2111-211-2-211111100-2-200000000110
χ5322222222222-1-12-1-1-12-1-122-1-1-1-1-1-100-2-200000000110-2-2-2-2-2-2-2-2-2-2-211-2111-211-2-2111111002200000000-1-10
χ542222222222-122-1-1-12-1-1-1-1-122-1-1-1-100002200000-100-1-2-2-2-2-2-2-2-2-2-21-2-2111-211111-2-211110000-2-2000001001
χ552222222222-122-1-1-12-1-1-1-1-122-1-1-1-10000-2-2000001001-2-2-2-2-2-2-2-2-2-21-2-2111-211111-2-2111100002200000-100-1
χ562222222-2-2-22-1-12-1-1-12-1-1-2-2111111002-200000000-110-2-2-2-2-2-2-2222-211-2111-21122-1-1-1-1-1-100-22000000001-10
χ572222222-2-2-22-1-12-1-1-12-1-1-2-211111100-22000000001-10-2-2-2-2-2-2-2222-211-2111-21122-1-1-1-1-1-1002-200000000-110
χ582222222-2-2-2-122-1-1-12-1-1-111-2-2111100002-200000-1001-2-2-2-2-2-2-22221-2-2111-2111-1-122-1-1-1-10000-2200000100-1
χ592222222-2-2-2-122-1-1-12-1-1-111-2-211110000-2200000100-1-2-2-2-2-2-2-22221-2-2111-2111-1-122-1-1-1-100002-200000-1001
χ60222-22-2-2000222222-2-2-2-2000000002-2000020-2000000-2-2-22-222000-2-2-2-2-2-2222200000000-220000-202000000
χ61222-22-2-2000222222-2-2-2-200000000-220000-202000000-2-2-22-222000-2-2-2-2-2-22222000000002-2000020-2000000
χ624444444444-2-2-2-211-2-211-2-2-2-21111000000000000000-4-4-4-4-4-4-4-4-4-42222-1-122-1-12222-1-1-1-1000000000000000
χ634444444-4-4-4-2-2-2-211-2-2112222-1-1-1-1000000000000000-4-4-4-4-4-4-44442222-1-122-1-1-2-2-2-21111000000000000000
χ64444-44-4-40004-2-24-2-22-42200000000000000000000000-4-4-44-444000-422-422-24-2-200000000000000000000000
χ65444-44-4-4000-244-2-2-2-422200000000000000000000000-4-4-44-4440002-4-42224-2-2-200000000000000000000000
χ66444-44-4-4000-2-2-2-21122-1-100003i3i−3i−3i000000000000000-4-4-44-4440002222-1-1-2-2110000−3i−3i3i3i000000000000000
χ67444-44-4-4000-2-2-2-21122-1-10000−3i−3i3i3i000000000000000-4-4-44-4440002222-1-1-2-21100003i3i−3i−3i000000000000000
χ684-440-40000044-4-44-4000000000000000000000000000-44-40400000-4-444-44000000000000000000000000000
χ694-440-4000004-22-4-22000000i6−i6i6−i6i6−i6000000000000000-44-40400000-42-242-2000000−i6i6−i6i6−i6i6000000000000000
χ704-440-4000004-22-4-22000000−i6i6−i6i6−i6i6000000000000000-44-40400000-42-242-2000000i6−i6i6−i6i6−i6000000000000000
χ714-440-400000-24-42-2200006−6006−6−66000000000000000-44-404000002-44-22-20000−6600−666−6000000000000000
χ724-440-400000-24-42-220000−6600−666−6000000000000000-44-404000002-44-22-200006−6006−6−66000000000000000
χ734-440-400000-2-2221-1003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000-44-4040000022-2-2-1100−3i3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000
χ744-440-400000-2-2221-1003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000-44-4040000022-2-2-1100−3i3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000
χ754-440-400000-2-2221-100−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000-44-4040000022-2-2-11003i−3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000
χ764-440-400000-2-2221-100−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000-44-4040000022-2-2-11003i−3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000
χ7766-36-3-3-36-3-3000000000000000000220000-12-1-1-10000-6-63-6333-633000000000000000000-2-200001-21110000
χ7866-36-3-3-36-3-3000000000000000000-2-200001-21110000-6-63-6333-633000000000000000000220000-12-1-1-10000
χ7966-36-3-3-3-633000000000000000000220000-1-2-1110000-6-63-63336-3-3000000000000000000-2-20000121-1-10000
χ8066-36-3-3-3-633000000000000000000-2-20000121-1-10000-6-63-63336-3-3000000000000000000220000-1-2-1110000
χ8166-3-6-333033−330000000000000000002-20000-1013−30000-6-6363-3-30−3333000000000000000000-22000010-1−330000
χ8266-3-6-333033−33000000000000000000-22000010-1−330000-6-6363-3-30−33330000000000000000002-20000-1013−30000
χ8366-3-6-3330−33330000000000000000002-20000-101−330000-6-6363-3-3033−33000000000000000000-22000010-13−30000
χ8466-3-6-3330−3333000000000000000000-22000010-13−30000-6-6363-3-3033−330000000000000000002-20000-101−330000
χ8512-12-60663−63000000000000000000000000000000000000-121260-6−6363000000000000000000000000000000000000
χ8612-12-606−6363000000000000000000000000000000000000-121260-663−63000000000000000000000000000000000000

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