Finite Group Databasebeta

← Group #13155745

Character table — Group #13155745

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order1244233346661212121212123336666666612121212121212121212123666661212121212122244441212121212121212121212121212121266666666121212121212121288888824242424888824242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111-11-11111111111111111111-11-111-1-11-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-111-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111111111111111111-11-11111111111111111111-11-11-1-111-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-11-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
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
χ911-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-111-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1i−ii−i1-111-1-1ii−i−ii−ii−i
χ1011-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-111-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−ii−ii1-111-1-1−i−iii−ii−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-11-1-11i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1-11-11-1-111i−i−ii-11-1-111−i−iiii−i−ii
χ1211-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-11-1-11−ii−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1-11-11-1-111−iii−i-11-1-111ii−i−i−iii−i
χ1311-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-111-1i−iiiiiiiii−i−i−i−i−i−i−i−i-11-11-1-1111-11-111-1-1−iii−i-11-1-111−i−iii−iii−i
χ1411-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-111-1−ii−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-1111-11-111-1-1i−i−ii-11-1-111ii−i−ii−i−ii
χ1511-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-111i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−ii−ii1-111-1-1ii−i−i−ii−ii
χ1611-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-111−ii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111i−ii−i1-111-1-1−i−iiii−ii−i
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χ202222222-1222-1-1-122222-1-1-122222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000000-2-2111111-2-2111111000022-1-1-1-100000000
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χ22222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-1-1-122-1-12-12-1-1-1-12-1-1-1-1-10202-2-2-2-2111111-2-21111110-10200-1-10-10200-1-100-2-200000000000011
χ23222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-1-1-122-1-12-12-1-1-1-12-1-1-1-1-10-20-22222-1-1-1-1-1-122-1-1-1-1-1-1010-20011010-2001100-2-200000000000011
χ24222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-1-1-122-1-12-12-1-1-1-12-1-1-1-1-10-20-2-2-2-2-2111111-2-2111111010-20011010-200110022000000000000-1-1
χ2522222-1222-12222-1-122-1-122-1-12-1-1-12-12-1-1-1-1-1-1222-1-12-1-1-1-12-1-1-1-1202022-1-122-1-1-1-1-1-122-1-1-1-1-1020-1-100-1020-1-10022000000000000-1-100
χ2622222-1222-12222-1-122-1-122-1-12-1-1-12-12-1-1-1-1-1-1222-1-12-1-1-1-12-1-1-1-12020-2-211-2-2111111-2-21111-1020-1-100-1020-1-100-2-20000000000001100
χ2722222-1222-12222-1-122-1-122-1-12-1-1-12-12-1-1-1-1-1-1222-1-12-1-1-1-12-1-1-1-1-20-2022-1-122-1-1-1-1-1-122-1-1-1-110-20110010-201100-2-20000000000001100
χ2822222-1222-12222-1-122-1-122-1-12-1-1-12-12-1-1-1-1-1-1222-1-12-1-1-1-12-1-1-1-1-20-20-2-211-2-2111111-2-2111110-20110010-20110022000000000000-1-100
χ292222-2222-2222222222222-22-2-2-2-222-2-2-2-2222222-22-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000000000002-22-20000
χ302222-2222-2222222222222-22-2-2-2-222-2-2-2-2222222-22-2-2-2-22-2-2-2-222000000000000000000000000000000000000000000000000-22-220000
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χ3322-2-2-222-1222-111-2-2-2-22-1-112-2-2-2-2-1-12222-2-21111-1-11111-1-1-1-1-11122-2-200000000000000000022-1-1-1-1-1-1-2-211111100002-2-1-11100000000
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χ3822-2-2-22-1222-12-2-2-2-211-12-1-2-1-21112-12-1-1-111-2-2112-1-2111-12-1-1-111020-2−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i0-10200-1-1010-2001100−2i2i000000000000i−i
χ3922-2-2-22-1222-12-2-2-2-211-12-1-2-1-21112-12-1-1-111-2-2112-1-2111-12-1-1-1110-2022i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii010-200110-10200-1-100−2i2i000000000000i−i
χ4022-2-2-22-1222-12-2-2-2-211-12-1-2-1-21112-12-1-1-111-2-2112-1-2111-12-1-1-1110-202−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i010-200110-10200-1-1002i−2i000000000000−ii
χ4122-2-2-2-1222-122-2-211-2-2-1-12-2-11-211-12-12-1-11111-2-22-11-211-1-12-1-11120-202i−2i−i−i2i2i−i−i−i−iii−2i−2iiiii-1020-1-10010-2011002i−2i000000000000−ii00
χ4222-2-2-2-1222-122-2-211-2-2-1-12-2-11-211-12-12-1-11111-2-22-11-211-1-12-1-11120-20−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−i-1020-1-10010-201100−2i2i000000000000i−i00
χ4322-2-2-2-1222-122-2-211-2-2-1-12-2-11-211-12-12-1-11111-2-22-11-211-1-12-1-111-20202i−2i−i−i2i2i−i−i−i−iii−2i−2iiiii10-201100-1020-1-100−2i2i000000000000i−i00
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.