Finite Group Databasebeta

← Group #13154844

Character table — Group #13154844

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222444444444444444444888888888888888812121212121212121212121212121212121218181818181818183636363636363636363636363636108108108108108108
order122222366633666666666666666633666666666666664412121212121212121212121212121212444412121212888812122424242424242424228888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1−i−iii
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii11ii−i−i
χ911-1-11-111-1-1111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1011-1-11-111-1-1111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1111-1-11-111-1-1111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23-11−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-1-11-111-1-1111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23-11ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-1-11-111-1-1111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13-11ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1411-1-11-111-1-1111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-11−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1511-1-11-111-1-1111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1611-1-11-111-1-1111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ17222222-1-1-1-122-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000
χ18222222-1-1-1-122-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-2-2-2-2-1-111111111000000
χ19222222-1-1-1-122-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-211112i2i−2i−2i11−i−i−i−iiiii000000
χ20222222-1-1-1-122-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-21111−2i−2i2i2i11iiii−i−i−i−i000000
χ212222-2-2222222-2-222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000022-2-222220000-2-200000000000000
χ222222-2-2222222-2-222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000-2-222-2-2-2-200002200000000000000
χ232222-2-2-1-1-1-1221122-2-2-2-222-2-2-2-222-1-1-1-11111-1-1-1-1111100000000000000000022-2-2-1-1-1-1000011−i3i3−i3i3−i3i3−i3i3000000
χ242222-2-2-1-1-1-1221122-2-2-2-222-2-2-2-222-1-1-1-11111-1-1-1-1111100000000000000000022-2-2-1-1-1-1000011i3−i3i3−i3i3−i3i3−i3000000
χ252222-2-2-1-1-1-1221122-2-2-2-222-2-2-2-222-1-1-1-11111-1-1-1-11111000000000000000000-2-22211110000-1-13−33−3−33−33000000
χ262222-2-2-1-1-1-1221122-2-2-2-222-2-2-2-222-1-1-1-11111-1-1-1-11111000000000000000000-2-22211110000-1-1−33−333−33−3000000
χ2722-2-22-2-1-11122-11222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000002i−2i2i−2i−i−iii2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000
χ2822-2-22-2-1-11122-11222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000002i−2i2i−2i−i−iii−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−iiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000
χ2922-2-22-2-1-11122-11222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000−2i2i−2i2iii−i−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000
χ3022-2-22-2-1-11122-11222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000−2i2i−2i2iii−i−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000
χ3122-2-2-2222-2-222-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222220000000000000000002i−2i−2i2i2i2i−2i−2i0000−2i2i00000000000000
χ3222-2-2-2222-2-222-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-22222000000000000000000−2i2i2i−2i−2i−2i2i2i00002i−2i00000000000000
χ3322-2-2-22-1-111221-122-2-2-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-10000000000000000002i−2i−2i2i−i−iii0000i−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000
χ3422-2-2-22-1-111221-122-2-2-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-10000000000000000002i−2i−2i2i−i−iii0000i−iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000
χ3522-2-2-22-1-111221-122-2-2-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-1000000000000000000−2i2i2i−2iii−i−i0000−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000
χ3622-2-2-22-1-111221-122-2-2-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-1000000000000000000−2i2i2i−2iii−i−i0000−ii−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000
χ3744444444441-2441-211-2-21-211-2-21-21-21-211-2-211-2-211-2-2441111-2-2-2-21111-2-2-2-20000000000000000000000000000
χ3844444444441-2441-211-2-21-211-2-21-21-21-211-2-211-2-211-2-2-4-4-1-1-1-12222-1-1-1-122220000000000000000000000000000
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χ414444-4-444441-2-4-41-2-1-1221-2-1-1221-21-21-2-1-12211-2-2-1-1220033-3-3000033-3-300000000000000000000000000000000
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χ444444-4-44444-21-4-4-2122-1-1-2122-1-1-21-21-2122-1-1-2-21122-1-1000000-3-3330000-3-3330000000000000000000000000000
χ4544-4-44-444-4-41-24-41-211-2-2-12-1-122-121-21-211-2-2-1-122-1-1224i−4iiiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i0000000000000000000000000000
χ4644-4-44-444-4-41-24-41-211-2-2-12-1-122-121-21-211-2-2-1-122-1-122−4i4i−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i0000000000000000000000000000
χ4744-4-44-444-4-4-214-4-21-2-2112-122-1-12-1-21-21-2-21122-1-122-1-14i−4i−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000
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χ4944-4-4-4444-4-41-2-441-2-1-122-1211-2-2-121-21-2-1-122-1-12211-2-2003i3i−3i−3i0000−3i−3i3i3i00000000000000000000000000000000
χ5044-4-4-4444-4-41-2-441-2-1-122-1211-2-2-121-21-2-1-122-1-12211-2-200−3i−3i3i3i00003i3i−3i−3i00000000000000000000000000000000
χ5144-4-4-4444-4-4-21-44-2122-1-12-1-2-2112-1-21-2122-1-122-1-1-2-2110000003i3i−3i−3i0000−3i−3i3i3i0000000000000000000000000000
χ5244-4-4-4444-4-4-21-44-2122-1-12-1-2-2112-1-21-2122-1-122-1-1-2-211000000−3i−3i3i3i00003i3i−3i−3i0000000000000000000000000000
χ534-44-4004-44-41-200-123-300-123-3001-21-2-123-3001-12-23-30000−i3i3−i3i300−2i32i3−i3i3−i3i300−2i32i30000000000000000000000000000
χ544-44-4004-44-41-200-123-300-123-3001-21-2-123-3001-12-23-30000i3−i3i3−i3002i3−2i3i3−i3i3−i3002i3−2i30000000000000000000000000000
χ554-44-4004-44-41-200-12-3300-12-33001-21-2-12-33001-12-2-330000−i3i3i3−i3−2i32i300−i3i3i3−i3−2i32i3000000000000000000000000000000
χ564-44-4004-44-41-200-12-3300-12-33001-21-2-12-33001-12-2-330000i3−i3−i3i32i3−2i300i3−i3−i3i32i3−2i3000000000000000000000000000000
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χ614-44-4004-44-4-21002-100-332-100-33-21-212-100-33-22-1100-33002i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i30000000000000000000000000000
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χ908-8-8800-444-4-42004-200-66-42006-64-22-1-21003-3-22-1100-330000000000000000000000000000000000000000000000

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