Finite Group Databasebeta

← Group #13137359

Character table — Group #13137359

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order122234444446661212121212121212121212123366666636661212121212121212121212121212121212121212121212128888888824242424242424242424242424242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ611111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ711111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-12-1-122-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
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χ1122222222222222222222222222-12-122-1-12-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ1222222222222222222222222222-12-122-1-12-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ132222222-2-2-2-22222222-2-2-2-2-2-2-2-2222222222222-2-222-2-2-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
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χ152222222-2-2-2-22222222-2-2-2-2-2-2-2-22-12-1-122-1-1-1-1-1-2-2-1-1111122-2-21111-1-1-1-111110000000000000000000000000000i3−i3i3−i30000
χ162222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-122-1-12-1-1-1-11122-2-2-2-2-1-1111111-1-1-1-1111100000000000000000000000000000000−i3i3−i3i3
χ172222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-122-1-12-1-1-1-11122-2-2-2-2-1-1111111-1-1-1-1111100000000000000000000000000000000i3−i3i3−i3
χ1822222-2-222-2-2222-2-2-2-22222-2-2-2-2222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ1922222-2-222-2-2222-2-2-2-22222-2-2-2-22-12-1-122-1-1-1-1-1-2-211-1-111-2-22211111111-1-1-1-10000000000000000000000000000−i3i3i3−i30000
χ2022222-2-222-2-2222-2-2-2-22222-2-2-2-22-12-1-122-1-1-1-1-1-2-211-1-111-2-22211111111-1-1-1-10000000000000000000000000000i3−i3−i3i30000
χ2122222-2-222-2-2222-2-2-2-22222-2-2-2-2-12-122-1-12-1-1-1-111-2-222-2-211-1-111111111-1-1-1-100000000000000000000000000000000−i3i3i3−i3
χ2222222-2-222-2-2222-2-2-2-22222-2-2-2-2-12-122-1-12-1-1-1-111-2-222-2-211-1-111111111-1-1-1-100000000000000000000000000000000i3−i3−i3i3
χ2322222-2-2-2-222222-2-2-2-2-2-2-2-222222-12-1-122-1-1-1-1-1221111-1-1-2-2-2-2-1-1-1-1111111110000000000000000000000002-200-1-1110000
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χ2622222-2-2-2-222222-2-2-2-2-2-2-2-22222-12-122-1-12-1-1-1-1-1-1-2-2-2-2221111-1-1-1-11111111100000000000000000000000000-22000011-1-1
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χ332-22-220000-22-22-200000000-2-222222-2-2-2-222-22-2-220000-220000-2-222000000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000000000000000
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χ916-6-66-36i−6i000033-3−3i−3i3i3i−3i33i33i3−3i3−333333−33000000000000000000000000000000000000−i2i2i2−i22−2−22ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ926-6-66-36i−6i000033-3−3i−3i3i3i−3i33i33i3−3i3−333333−33000000000000000000000000000000000000i2−i2−i2i2−222−2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ936-6-66-36i−6i000033-3−3i−3i3i3i3i3−3i3−3i33i333−33−3333000000000000000000000000000000000000−i2i2i2−i22−2−22ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ946-6-66-36i−6i000033-3−3i−3i3i3i3i3−3i3−3i33i333−33−3333000000000000000000000000000000000000i2−i2−i2i2−222−2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ956-6-66-3−6i6i000033-33i3i−3i−3i−3i33i33i3−3i333−33−3333000000000000000000000000000000000000−i2i2i2−i2−222−2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ966-6-66-3−6i6i000033-33i3i−3i−3i−3i33i33i3−3i333−33−3333000000000000000000000000000000000000i2−i2−i2i22−2−22−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ976-6-66-3−6i6i000033-33i3i−3i−3i3i3−3i3−3i33i3−333333−33000000000000000000000000000000000000−i2i2i2−i2−222−2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ986-6-66-3−6i6i000033-33i3i−3i−3i3i3−3i3−3i33i3−333333−33000000000000000000000000000000000000i2−i2−i2i22−2−22−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000

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