Finite Group Databasebeta

← Group #13155758

Character table — Group #13155758

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order1244233346661212121212123336666666612121212121212121212123666661212121212124488881212121212121212121212121212121224242424242424242424242424242424224488242424248888661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-111-1-11111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11-11-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-111-1-111-1-1-1-11111-11-11-1-1-1-1-1-1-1-1-1-1-11-11
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ51111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-11-11-1-1-1-1-1-11111-11-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-11-1-1-1-1-1-1-111111-11-1
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ911-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1i−ii−ii−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−ii−ii−iii−i−iii−i−i11-1-11-111-1-1ii−i−i11-1-1
χ1011-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1i−ii−i−iiiiiiiiii−i−i−i−i−i−i−i−ii−i−iii−i−iiii−i−i−i−iii1-1-11-11-1-111−i−iii1-1-11
χ1111-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1i−i−iii−iiiiiiiii−i−i−i−i−i−i−i−i−iii−i−iii−i−i−iiiii−i−i-111-1-11-1-111−i−iii-111-1
χ1211-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1i−i−ii−iiiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−ii−ii−i−iii−i−iii-1-1111-111-1-1ii−i−i-1-111
χ1311-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1−iii−ii−i−i−i−i−i−i−i−i−iiiiiiiiii−ii−ii−ii−iii−i−iii−i−i-1-1111-111-1-1−i−iii-1-111
χ1411-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1−iii−i−ii−i−i−i−i−i−i−i−iiiiiiiiii−i−iii−i−iiii−i−i−i−iii-111-1-11-1-111ii−i−i-111-1
χ1511-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1−ii−iii−i−i−i−i−i−i−i−i−iiiiiiiii−iii−i−iii−i−i−iiiii−i−i1-1-11-11-1-111ii−i−i1-1-11
χ1611-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1−ii−ii−ii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−ii−ii−i−iii−i−iii11-1-11-111-1-1−i−iii11-1-1
χ172222222-1222-122-1-1222-1-122-1-12-1-1-12-1-1-1-1-122-1-12-12-1-1-1-12-1-1-1-1-122002222-1-1-1-1-1-122-1-1-1-1-1-100-1-100220000-1-1-1-1020200000000000-10-1
χ182222222-1222-122-1-1222-1-122-1-12-1-1-12-1-1-1-1-122-1-12-12-1-1-1-12-1-1-1-1-12200-2-222-1-1-1-1-1-122-1-1-1-1-1-1001100-2-2000011110-20-200000000000101
χ192222222-1222-122-1-1222-1-122-1-12-1-1-12-1-1-1-1-122-1-12-12-1-1-1-12-1-1-1-1-1-2-20022-2-2111111-2-211111100-1-100220000-1-1-1-10-20-200000000000101
χ202222222-1222-122-1-1222-1-122-1-12-1-1-12-1-1-1-1-122-1-12-12-1-1-1-12-1-1-1-1-1-2-200-2-2-2-2111111-2-2111111001100-2-200001111020200000000000-10-1
χ21222222-1222-12-1-12222-12-12-12-1-12-1-1-12-1-1-1-1-1-1222-1-12-1-1-1-12-1-1-1-1222200-1-122-1-1-1-1-1-122-1-1-1-1-1-1002200-1-1-1-1000020200000000000-10-10
χ22222222-1222-12-1-12222-12-12-12-1-12-1-1-12-1-1-1-1-1-1222-1-12-1-1-1-12-1-1-1-122-2-200-1-122-1-1-1-1-1-122-1-1-1-11100-2-20011110000-20-2000000000001010
χ23222222-1222-12-1-12222-12-12-12-1-12-1-1-12-1-1-1-1-1-1222-1-12-1-1-1-12-1-1-1-1-2-2220011-2-2111111-2-21111-1-1002200-1-1-1-10000-20-2000000000001010
χ24222222-1222-12-1-12222-12-12-12-1-12-1-1-12-1-1-1-1-1-1222-1-12-1-1-1-12-1-1-1-1-2-2-2-20011-2-2111111-2-211111100-2-2001111000020200000000000-10-10
χ2522222-1222-1222222-1-1-1-12-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100222200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000
χ2622222-1222-1222222-1-1-1-12-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022-2-2000000000000000022-2-2-1-111-1-1-1-111110000-2-2111100000000
χ2722222-1222-1222222-1-1-1-12-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2220000000000000000-2-22211-1-11111-1-1-1-10000-2-2111100000000
χ2822222-1222-1222222-1-1-1-12-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000000000-2-2-2-2111111111111000022-1-1-1-100000000
χ292222-2222-2222222222222-2222-2-2-2-2-2-2-2-2222222-22-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000000000002-22-20000
χ302222-2222-2222222222222-2222-2-2-2-2-2-2-2-2222222-22-2-2-2-22-2-2-2-222000000000000000000000000000000000000000000000000-22-220000
χ3122-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
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χ3322-2-2-222-1222-1-2-211-2-22-1-1-22-1-1-21112-1-1-111-2-2112-1-2111-12-1-1-1112i−2i002i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii00−ii002i−2i0000−i−iii020-200000000000-101
χ3422-2-2-222-1222-1-2-211-2-22-1-1-22-1-1-21112-1-1-111-2-2112-1-2111-12-1-1-1112i−2i00−2i2i2i2i−i−i−i−i−i−i−2i−2iiiiiii00i−i00−2i2i0000ii−i−i0-2020000000000010-1
χ3522-2-2-222-1222-1-2-211-2-22-1-1-22-1-1-21112-1-1-111-2-2112-1-2111-12-1-1-111−2i2i002i−2i−2i−2iiiiiii2i2i−i−i−i−i−i−i00−ii002i−2i0000−i−iii0-2020000000000010-1
χ3622-2-2-222-1222-1-2-211-2-22-1-1-22-1-1-21112-1-1-111-2-2112-1-2111-12-1-1-111−2i2i00−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i00i−i00−2i2i0000ii−i−i020-200000000000-101
χ3722-2-2-22-1222-1211-2-2-2-2-12-1-2-12-11-211-12-1-11111-2-22-11-211-1-12-1-1112i−2i2i−2i00−i−i2i2i−i−i−i−iii−2i−2iiiii−ii002i−2i00−i−iii000020-200000000000-1010
χ3822-2-2-22-1222-1211-2-2-2-2-12-1-2-12-11-211-12-1-11111-2-22-11-211-1-12-1-1112i−2i−2i2i00−i−i2i2i−i−i−i−iii−2i−2iiiiii−i00−2i2i00ii−i−i0000-2020000000000010-10
χ3922-2-2-22-1222-1211-2-2-2-2-12-1-2-12-11-211-12-1-11111-2-22-11-211-1-12-1-111−2i2i2i−2i00ii−2i−2iiiii−i−i2i2i−i−i−i−i−ii002i−2i00−i−iii0000-2020000000000010-10
χ4022-2-2-22-1222-1211-2-2-2-2-12-1-2-12-11-211-12-1-11111-2-22-11-211-1-12-1-111−2i2i−2i2i00ii−2i−2iiiii−i−i2i2i−i−i−i−ii−i00−2i2i00ii−i−i000020-200000000000-1010
χ4122-2-2-2-1222-122-2-2-2-211-1-121-1-12-2-2-2-22222-2-21111-1-11111-1-1-1-1-111002i−2i2i−2i00000000000000002i−2i2i−2i−ii−ii−i−iii−i−iii00002-2-1-11100000000
χ4222-2-2-2-1222-122-2-2-2-211-1-121-1-12-2-2-2-22222-2-21111-1-11111-1-1-1-1-111002i−2i−2i2i00000000000000002i−2i−2i2i−iii−i−i−iiiii−i−i0000-2211-1-100000000
χ4322-2-2-2-1222-122-2-2-2-211-1-121-1-12-2-2-2-22222-2-21111-1-11111-1-1-1-1-11100−2i2i2i−2i0000000000000000−2i2i2i−2ii−i−iiii−i−i−i−iii0000-2211-1-100000000
χ4422-2-2-2-1222-122-2-2-2-211-1-121-1-12-2-2-2-22222-2-21111-1-11111-1-1-1-1-11100−2i2i−2i2i0000000000000000−2i2i−2i2ii−ii−iii−i−iii−i−i00002-2-1-11100000000
χ45444444-2-244-2-2-2-2-2-244-2-214-2-21-2-211-2-21111-2-2-2-241-2-2111-2-21111440000-2-2-2-21111-2-2-2-211110000000000000000000000000000000000
χ46444444-2-244-2-2-2-2-2-244-2-214-2-21-2-211-2-21111-2-2-2-241-2-2111-2-21111-4-400002222-1-1-1-12222-1-1-1-10000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.