Finite Group Databasebeta

← Group #72230634

Character table — Group #72230634

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122233444444444444444444444444468888888888888888888888881212121212121212121212121212121212121212121212122525505050505050507575100100100100100150150150150150
order1223644555555610101010101010101010101010101010101041515151515153030303030303030303030303030303030302020202020202020202020202020202020202020202020202224444664461212121244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1ii−i−i-1-1-1-1-1ii−i−i-1ii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1−i−iii-1-1-1-1-1−i−iii-1−i−iii
χ511111-1-11111111111111111111111111-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1
χ611111-1-11111111111111111111111111-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-1-1-1-1-11111
χ711111-1-11111111111111111111111111-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111-1ii−i−i1−i−iii
χ811111-1-11111111111111111111111111-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-111-1−i−iii1ii−i−i
χ911-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-11-11111-11-11-1-11-11-1
χ1011-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111111-1-11-11-1-11-11
χ1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11i−i−ii-1-1-1-11i−i−ii1i−i−ii
χ1211-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11−iii−i-1-1-1-11−iii−i1−iii−i
χ1311-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11-11-111-1-1-11-11-11-11-11
χ1411-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-1111-1-1-1-11-1111-11-1
χ1511-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11i−i−ii-1-1111i−i−ii-1−iii−i
χ1611-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11−iii−i-1-1111−iii−i-1i−i−ii
χ17222-1-100222222-12222222222222222220-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002222222-1-100-1-1-1-1-100000
χ18222-1-100222222-12222222222222222220-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000222-2-2-2-2-1-100-1111100000
χ19222-1-100222222-12222222222222222220-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-22i2i−2i−2i11001−i−iii00000
χ20222-1-100222222-12222222222222222220-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2−2i−2i2i2i11001ii−i−i00000
χ2122-2-1-1002222221-2-2-2-2-2-2-2-2-2-2-2-22222220-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000022-22-22-2-1-1001-11-1100000
χ2222-2-1-1002222221-2-2-2-2-2-2-2-2-2-2-2-22222220-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000022-2-22-22-1-10011-11-100000
χ2322-2-1-1002222221-2-2-2-2-2-2-2-2-2-2-2-22222220-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-2-222i−2i−2i2i1100-1−iii−i00000
χ2422-2-1-1002222221-2-2-2-2-2-2-2-2-2-2-2-22222220-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-2-22−2i2i2i−2i1100-1i−i−ii00000
χ252-202-22i−2i2222220000000000000-2-2-2-2-2-20222222-2-2-2-2-2-20000000000002i2i2i2i2i2i−2i−2i−2i−2i−2i−2i0000000000002-2000002-22i−2i0000000000
χ262-202-22i−2i2222220000000000000-2-2-2-2-2-20222222-2-2-2-2-2-20000000000002i2i2i2i2i2i−2i−2i−2i−2i−2i−2i000000000000-2200000-22−2i2i0000000000
χ272-202-2−2i2i2222220000000000000-2-2-2-2-2-20222222-2-2-2-2-2-2000000000000−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i0000000000002-2000002-2−2i2i0000000000
χ282-202-2−2i2i2222220000000000000-2-2-2-2-2-20222222-2-2-2-2-2-2000000000000−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i000000000000-2200000-222i−2i0000000000
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χ3544444-4-44-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-14-1-1-1-1-1-44-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-411111-411111-4-41111111111000000000000000000000
χ3644444-4-4-14-1-1-1-14-1-144-1-1-1-1-1-1-1-1-14-1-1-1-1-4-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-11-411111-4111111-4-411111111000000000000000000000
χ3744444-4-4-1-1−1+53−523+52−1−54-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1−1+53−523+52−1−5-4-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5111−5−3+52−3−521+5111−5−3+52−3−521+511111−51−5−3+52−3+52−3−52−3−521+51+5000000000000000000000
χ3844444-4-4-1-13−52−1−5−1+53+524-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-13−52−1−5−1+53+52-4-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+5211−3+521+51−5−3−5211−3+521+51−5−3−521111−3+52−3+521+51+51−51−5−3−52−3−52000000000000000000000
χ3944444-4-4-1-13+52−1+5−1−53−524-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-13+52−1+5−1−53−52-4-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−5211−3−521−51+5−3+5211−3−521−51+5−3+521111−3−52−3−521−51−51+51+5−3+52−3+52000000000000000000000
χ4044444-4-4-1-1−1−53+523−52−1+54-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1−1−53+523−52−1+5-4-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5111+5−3−52−3+521−5111+5−3−52−3+521−511111+51+5−3−52−3−52−3+52−3+521−51−5000000000000000000000
χ4144-444444-1-1-1-1-1-4-4-411111111114-1-1-1-1-1-44-1-1-1-1-14-1-1-1-1-1-4-411111111114-1-1-1-1-14-1-1-1-1-1-4-41111111111000000000000000000000
χ4244-44444-14-1-1-1-1-411-4-411111111-14-1-1-1-1-4-14-1-1-1-1-14-1-1-1-111-4-411111111-14-1-1-1-1-14-1-1-1-111-4-411111111000000000000000000000
χ4344-44444-1-1−1+53−523+52−1−5-411111−51−5−3+52−3+52−3−52−3−521+51+5-1-1−1+53−523+52−1−5-4-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+5000000000000000000000
χ4444-44444-1-13−52−1−5−1+53+52-41111−3+52−3+521+51+51−51−5−3−52−3−52-1-13−52−1−5−1+53+52-4-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−52000000000000000000000
χ4544-44444-1-13+52−1+5−1−53−52-41111−3−52−3−521−51−51+51+5−3+52−3+52-1-13+52−1+5−1−53−52-4-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+52000000000000000000000
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χ4844-444-4-4-14-1-1-1-1-411-4-411111111-14-1-1-1-14-14-1-1-1-1-14-1-1-1-111-4-4111111111-411111-41111-1-144-1-1-1-1-1-1-1-1000000000000000000000
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χ544-404-44i−4i4-1-1-1-1-1000−55−55−55−55−55-41111104-1-1-1-1-1-41111100−55−55−55−55−554i−i−i−i−i−i−4iiiiii00−i5i5−i5i5−i5i5−i5i5−i5i5000000000000000000000
χ554-404-44i−4i-14-1-1-1-105−5005−5−55−555−51-411110-14-1-1-1-11-411115−5005−5−55−555−5−i4i−i−i−i−ii−4iiiiii5−i500i5−i5−i5i5−i5i5i5−i5000000000000000000000
χ564-404-44i−4i-14-1-1-1-10−5500−555−55−5−551-411110-14-1-1-1-11-41111−5500−555−55−5−55−i4i−i−i−i−ii−4iiiii−i5i500−i5i5i5−i5i5−i5−i5i5000000000000000000000
χ574-404-44i−4i-1-1−1+53−523+52−1−505−5−55005+52−5−52−5+525−5200111−5−3+52−3−521+50-1-1−1+53−523+52−1−5111−5−3+52−3−521+55−5−55005+52−5−52−5+525−5200−i−i−2ζ11−2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−2ζ3−2ζ7ii2ζ11+2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ192ζ3+2ζ7i5−i5−i5i5003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ1900000000000000000000000
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χ1028-80-4400-2-2−2−253+53−5−2+250−252525−25005−5−5+5−5−55+500222+25−3−5−3+52−250111+5−3−52−3+521−5-1-1−1−53+523−52−1+55−5−5500−5+525−525+52−5−5200000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.