Finite Group Databasebeta

← Group #13156012

Character table — Group #13156012

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222222444444444444444444444488888888888812121212121212121212121212121212121212122424242424242424242424242424242424363636363636363654547272727272108
order12223334466666666633366666666612121212121212121212366612121212121212124488242424242424242424242424242424244121212121212121212121212121212122288242424244446612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-111-1-11
χ51111111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000002200000-2
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χ13222222-12222-1-1222-122-1-12-1-1-1-12-12-12-12-1-1-12-1-12-1-1-1-122-1-1-1-1-1-100-2-2-2-2-2-21111111111112000022-1-10000-1-1-1-1-2-200000000011000
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χ874-4-444-2400-424-44-2-4-42-24-224-4-2222-2-40000000000-2-22200000000002i2−2i2−i2i2−i2i22i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000000
χ884-4-444-2-200-42-224-2-422-2-212-221-12-1-220003i−3i00−3i3i011-1-100003i−3i−3i3i00−2i22i2i2−i2i2−i2i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23000000000000000000000000000000000
χ894-4-444-2-200-42-224-2-422-2-212-221-12-1-220003i−3i00−3i3i011-1-100003i−3i−3i3i002i2−2i2−i2i2−i2i2−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000000000000
χ904-4-444-2-200-42-224-2-422-2-212-221-12-1-22000−3i3i003i−3i011-1-10000−3i3i3i−3i00−2i22i2i2−i2i2−i2i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23000000000000000000000000000000000
χ914-4-444-2-200-42-224-2-422-2-212-221-12-1-22000−3i3i003i−3i011-1-10000−3i3i3i−3i002i2−2i2−i2i2−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000000000000000
χ924-4-44-244002-44-4-242-4-4-2-242-224-42-4-220000000000-2-22200000000000000000000000000000000000000000000000−2i22i2i2−i2i2−i200000000
χ934-4-44-244002-44-4-242-4-4-2-242-224-42-4-220000000000-2-222000000000000000000000000000000000000000000000002i2−2i2−i2i2−i2i200000000
χ948888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ958888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-48-8444444-4-4-4222-2-2-2-2-222-22-4-4-42244-2-24-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-4-88444444-4-4-4222-2-2-2-2-222-22444-2-2-4-422-4-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000
χ988-88-8-48-400-484-44-844-8-42-4-4-224-4444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4800-4-4-88444-842-4-424-44-4-24-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-400-4-44-4444442222-22-22-2-2-2-20006i−6i006i−6i0-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-400-4-44-4444442222-22-22-2-2-2-2000−6i6i00−6i6i0-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1028-8-88-48-4004-8-44-4844-8-42-442-2-4444-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-4800448-8-4-44-842-4-4-2-44-44-2424000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-40044-44-4-4444222-22-22-2-2-22-20006i−6i00−6i6i0-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-40044-44-4-4444222-22-22-2-2-22-2000−6i6i006i−6i0-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000

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