Finite Group Databasebeta

← Group #72230631

Character table — Group #72230631

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122224444444444444444444444448888888888888888888888881010101010101010101010102020202020202020202020202020202020202020202020202525252550505050150150150150150150150150
order1244361212551010151515152020202030303030606060606060606055101015151515202020203030303060606060606060602244666612121212101010102020202030303030303030306060606060606060224466121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111111111111111111111111111111111111111111111111111111-11-11-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ611111111111111111111111111111111111111111111111111111111-11-11-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ911-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-11-11-1
χ1011-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-11-11-11-11
χ1111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111i−ii−i−ii−ii
χ1211-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111−ii−iii−ii−i
χ1311-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111i−i−iii−i−ii
χ1411-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111−iii−i−iii−i
χ1511-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-11-111-1
χ1611-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-11-1-11
χ172222-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100000000
χ182222-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-22-2-1-111-1-11122-2-222-2-2-1-1-1-11111-1-1-1-11111-2-2-2-2111100000000
χ192222-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-22-2211-1-111-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-1-2-2-2-2111100000000
χ202222-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2-2-2-2-211111111111111112222-1-1-1-100000000
χ2122-2-2-1-1112222-1-1-1-1-2-2-2-2-1-1-1-1111111112222-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-1-11100000000
χ2222-2-2-1-1112222-1-1-1-1-2-2-2-2-1-1-1-1111111112222-1-1-1-1-2-2-2-2-1-1-1-1111111112-2-22-1-11111-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1-2-22211-1-100000000
χ2322-2-2-1-1112222-1-1-1-1-2-2-2-2-1-1-1-1111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111-222-211-1-1-1-111-2-22222-2-21111-1-1-1-1-1-1-1-11111-2-22211-1-100000000
χ2422-2-2-1-1112222-1-1-1-1-2-2-2-2-1-1-1-1111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-122-2-2-1-11100000000
χ252-22i−2i2-22i−2i22-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000002-22i−2i2-22i−2i00000000
χ262-22i−2i2-22i−2i22-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000-22−2i2i-22−2i2i00000000
χ272-22i−2i-11−ii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000−i3i3−i3i33−33−300000000−i3−i3i3i3−i3−i3i3i333−3−333−3−32-22i−2i-11−ii00000000
χ282-22i−2i-11−ii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000−i3i3i3−i33−3−3300000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333-22−2i2i1-1i−i00000000
χ292-22i−2i-11−ii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000i3−i3−i3i3−333−300000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3-22−2i2i1-1i−i00000000
χ302-22i−2i-11−ii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000i3−i3i3−i3−33−3300000000i3i3−i3−i3i3i3−i3−i3−3−333−3−3332-22i−2i-11−ii00000000
χ312-2−2i2i2-2−2i2i22-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000002-2−2i2i2-2−2i2i00000000
χ322-2−2i2i2-2−2i2i22-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000-222i−2i-222i−2i00000000
χ332-2−2i2i-11i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000−i3i3−i3i3−33−3300000000−i3−i3i3i3−i3−i3i3i3−3−333−3−3332-2−2i2i-11i−i00000000
χ342-2−2i2i-11i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000−i3i3i3−i3−333−300000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3-222i−2i1-1−ii00000000
χ352-2−2i2i-11i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000i3−i3−i3i33−3−3300000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333-222i−2i1-1−ii00000000
χ362-2−2i2i-11i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000i3−i3i3−i33−33−300000000i3i3−i3−i3i3i3−i3−i333−3−333−3−32-2−2i2i-11i−i00000000
χ37444444444-14-144-1-14-14-144-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-104040044004400-1-100-1-10000-1-1-1-10000-1-1-1-10000000000000000
χ38444444444-14-144-1-14-14-144-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10-40-400-4-400-4-40011001100001111000011110000000000000000
χ3944444444-14-14-1-144-14-14-1-144-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1404044004400-1-100-1-100-1-1-1-10000-1-1-1-100000000000000000000
χ4044444444-14-14-1-144-14-14-1-144-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-40-40-4-400-4-4001100110011110000111100000000000000000000
χ414444-2-2-2-24-14-1-2-21−i1521+i1524-14-1-2-21−i1521+i152-2-21−i1521+i152-2-21−i1521+i152-1-1-1-11−i1521−i1521+i1521+i152-1-1-1-11−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152040400-2-200-2-200-1-100-1-100001−i1521+i1521−i1521+i15200001−i1521+i1521−i1521+i1520000000000000000
χ424444-2-2-2-24-14-1-2-21−i1521+i1524-14-1-2-21−i1521+i152-2-21−i1521+i152-2-21−i1521+i152-1-1-1-11−i1521−i1521+i1521+i152-1-1-1-11−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1520-40-400220022001100110000−1+i152−1−i152−1+i152−1−i1520000−1+i152−1−i152−1+i152−1−i1520000000000000000
χ434444-2-2-2-24-14-1-2-21+i1521−i1524-14-1-2-21+i1521−i152-2-21+i1521−i152-2-21+i1521−i152-1-1-1-11+i1521+i1521−i1521−i152-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152040400-2-200-2-200-1-100-1-100001+i1521−i1521+i1521−i15200001+i1521−i1521+i1521−i1520000000000000000
χ444444-2-2-2-24-14-1-2-21+i1521−i1524-14-1-2-21+i1521−i152-2-21+i1521−i152-2-21+i1521−i152-1-1-1-11+i1521+i1521−i1521−i152-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1520-40-400220022001100110000−1−i152−1+i152−1−i152−1+i1520000−1−i152−1+i152−1−i152−1+i1520000000000000000
χ454444-2-2-2-2-14-141−i1521+i152-2-2-14-141−i1521+i152-2-21−i1521+i152-2-21−i1521+i152-2-2-1-1-1-11−i1521+i1521−i1521+i152-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1524040-2-200-2-200-1-100-1-1001−i1521+i1521−i1521+i15200001−i1521+i1521−i1521+i15200000000000000000000
χ464444-2-2-2-2-14-141−i1521+i152-2-2-14-141−i1521+i152-2-21−i1521+i152-2-21−i1521+i152-2-2-1-1-1-11−i1521+i1521−i1521+i152-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-40-402200220011001100−1+i152−1−i152−1+i152−1−i1520000−1+i152−1−i152−1+i152−1−i15200000000000000000000
χ474444-2-2-2-2-14-141+i1521−i152-2-2-14-141+i1521−i152-2-21+i1521−i152-2-21+i1521−i152-2-2-1-1-1-11+i1521−i1521+i1521−i152-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1524040-2-200-2-200-1-100-1-1001+i1521−i1521+i1521−i15200001+i1521−i1521+i1521−i15200000000000000000000
χ484444-2-2-2-2-14-141+i1521−i152-2-2-14-141+i1521−i152-2-21+i1521−i152-2-21+i1521−i152-2-2-1-1-1-11+i1521−i1521+i1521−i152-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-40-402200220011001100−1−i152−1+i152−1−i152−1+i1520000−1−i152−1+i152−1−i152−1+i15200000000000000000000
χ4944-4-444-4-44-14-144-1-1-41-4144-1-1-4-411-4-411-1-1-1-1-1-1-1-11111-1-1-1-111111111040-4004400-4-400-1-100110000-1-1-1-1000011110000000000000000
χ5044-4-444-4-44-14-144-1-1-41-4144-1-1-4-411-4-411-1-1-1-1-1-1-1-11111-1-1-1-1111111110-40400-4-40044001100-1-1000011110000-1-1-1-10000000000000000
χ5144-4-444-4-4-14-14-1-1441-41-4-1-14411-4-411-4-4-1-1-1-1-1-1-1-11111-1-1-1-11111111140-404400-4-400-1-1001100-1-1-1-10000111100000000000000000000
χ5244-4-444-4-4-14-14-1-1441-41-4-1-14411-4-411-4-4-1-1-1-1-1-1-1-11111-1-1-1-111111111-4040-4-40044001100-1-10011110000-1-1-1-100000000000000000000
χ5344-4-4-2-2224-14-1-2-21−i1521+i152-41-41-2-21−i1521+i15222−1+i152−1−i15222−1+i152−1−i152-1-1-1-11−i1521−i1521+i1521+i15211111−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152040-400-2-2002200-1-1001100001−i1521+i1521−i1521+i1520000−1+i152−1−i152−1+i152−1−i1520000000000000000
χ5444-4-4-2-2224-14-1-2-21−i1521+i152-41-41-2-21−i1521+i15222−1+i152−1−i15222−1+i152−1−i152-1-1-1-11−i1521−i1521+i1521+i15211111−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i1520-404002200-2-2001100-1-10000−1+i152−1−i152−1+i152−1−i15200001−i1521+i1521−i1521+i1520000000000000000
χ5544-4-4-2-2224-14-1-2-21+i1521−i152-41-41-2-21+i1521−i15222−1−i152−1+i15222−1−i152−1+i152-1-1-1-11+i1521+i1521−i1521−i15211111+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152040-400-2-2002200-1-1001100001+i1521−i1521+i1521−i1520000−1−i152−1+i152−1−i152−1+i1520000000000000000
χ5644-4-4-2-2224-14-1-2-21+i1521−i152-41-41-2-21+i1521−i15222−1−i152−1+i15222−1−i152−1+i152-1-1-1-11+i1521+i1521−i1521−i15211111+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i1520-404002200-2-2001100-1-10000−1−i152−1+i152−1−i152−1+i15200001+i1521−i1521+i1521−i1520000000000000000
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χ1078-8−8i8i-444i−4i-2-2221+i151−i151−i151+i152i2i−2i−2i−1−i15−1+i15−1+i15−1−i15−2ζ19−2ζ23−2ζ31−2ζ47−2ζ7−2ζ11−2ζ43−2ζ59−2ζ7−2ζ11−2ζ43−2ζ59−2ζ19−2ζ23−2ζ31−2ζ472ζ19+2ζ23+2ζ31+2ζ472ζ7+2ζ11+2ζ43+2ζ592ζ7+2ζ11+2ζ43+2ζ592ζ19+2ζ23+2ζ31+2ζ47-232-31−3+i152−3−i15212i−3i−2i3i-13−i1523+i152-1−i2ζ7+2ζ11+ζ19+ζ23+ζ31+2ζ43+ζ47+2ζ59ζ7+ζ11+2ζ19+2ζ23+2ζ31+ζ43+2ζ47+ζ59−ii−2ζ7−2ζ11−ζ19−ζ23−ζ31−2ζ43−ζ47−2ζ59−ζ7−ζ11−2ζ19−2ζ23−2ζ31−ζ43−2ζ47−ζ59i0000000000000000000000000000000000000000000000000000
χ1088-8−8i8i-444i−4i-2-2221+i151−i151+i151−i152i2i−2i−2i−1−i15−1+i15−1−i15−1+i15−2ζ19−2ζ23−2ζ31−2ζ47−2ζ7−2ζ11−2ζ43−2ζ59−2ζ19−2ζ23−2ζ31−2ζ47−2ζ7−2ζ11−2ζ43−2ζ592ζ19+2ζ23+2ζ31+2ζ472ζ7+2ζ11+2ζ43+2ζ592ζ19+2ζ23+2ζ31+2ζ472ζ7+2ζ11+2ζ43+2ζ593-2-32−3−i15211−3+i152−3i2i3i−2i3+i152-1-13−i152ζ7+ζ11+2ζ19+2ζ23+2ζ31+ζ43+2ζ47+ζ59−i−i2ζ7+2ζ11+ζ19+ζ23+ζ31+2ζ43+ζ47+2ζ59−ζ7−ζ11−2ζ19−2ζ23−2ζ31−ζ43−2ζ47−ζ59ii−2ζ7−2ζ11−ζ19−ζ23−ζ31−2ζ43−ζ47−2ζ590000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.