Finite Group Databasebeta

← Group #72231331

Character table — Group #72231331

Order 3600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
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order1333555515151515151515151515151515151515151515151515151522266444461212121210102666101010103030303030303030303030303030303030303030303030302226644446121212121010
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111111111111111111111111111111111111-1-1-1-11-1-1-1-111
χ3111111111111111111111111111111111-1-11111-1-1111-1-1-1-1111111111111111111111111111111111-1-11111-1-1111-1-1-1-1
χ4111111111111111111111111111111111-1-111-1-1111-1-111-1-1111111111111111111111111111111111-1-111-1-1111-1-111-1-1
χ511111111111111111111111111111111-11-1-1-1i−ii−i-1i−ii−i1-111111111111111111111111111111111-11-1-1-1i−ii−i-1i−ii−i1-1
χ611111111111111111111111111111111-11-1-1-1−ii−ii-1−ii−ii1-111111111111111111111111111111111-11-1-1-1−ii−ii-1−ii−ii1-1
χ711111111111111111111111111111111-1-11-1-1i−i−ii-1i−i−ii-1111111111111111111111111111111111-1-11-1-1i−i−ii-1i−i−ii-11
χ811111111111111111111111111111111-1-11-1-1−iii−i-1−iii−i-1111111111111111111111111111111111-1-11-1-1−iii−i-1−iii−i-11
χ922-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12002-10022-100-1-10022-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12002-10022-100-1-100
χ1022-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12002-100-2-2-100110022-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12002-100-2-2-1001100
χ1122-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-200-21002i−2i100−ii0022-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-200-21002i−2i100−ii00
χ1222-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-200-2100−2i2i100i−i0022-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-200-2100−2i2i100i−i00
χ132-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-122200-1-1-100002-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-122200-1-1-10000
χ142-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-12-2-200-11100002-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-12-2-200-1110000
χ152-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2001-22i−2i001−ii00002-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2001-22i−2i001−ii0000
χ162-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2001-2−2i2i001i−i00002-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2001-2−2i2i001i−i0000
χ1744444-1-1-14-14-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1004000000000000-144444-1-1-14-14-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1004000000000000-1
χ1844444-1-1-14-14-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-4000000000000144444-1-1-14-14-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-40000000000001
χ194444-14-1-1-14-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-104000000000000-104444-14-1-1-14-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-104000000000000-10
χ204444-14-1-1-14-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10-4000000000000104444-14-1-1-14-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10-400000000000010
χ214-2-214444-2-2-2-21111-2-2-2-2-2-2-2-211111111400-2-2000010000004-2-214444-2-2-2-21111-2-2-2-2-2-2-2-211111111400-2-200001000000
χ224-2-214444-2-2-2-21111-2-2-2-2-2-2-2-211111111-400220000-10000004-2-214444-2-2-2-21111-2-2-2-2-2-2-2-211111111-400220000-1000000
χ238888-2-23-2-2-2-2-2-2-2-2-233-2-233-2-23333-2-2-2-200000000000000008888-2-23-2-2-2-2-2-2-2-2-233-2-233-2-23333-2-2-2-20000000000000000
χ248888-2-2-23-2-2-2-2-2-2-2-2-2-233-2-233-2-2-2-2333300000000000000008888-2-2-23-2-2-2-2-2-2-2-2-2-233-2-233-2-2-2-233330000000000000000
χ2588-4-48-2-2-28-2-41-4-411-2-2-2-2111111111111000000000000000088-4-48-2-2-28-2-41-4-411-2-2-2-21111111111110000000000000000
χ2688-4-4-28-2-2-281-411-4-4-2-2-2-2111111111111000000000000000088-4-4-28-2-2-281-411-4-4-2-2-2-21111111111110000000000000000
χ2788-4-4-2-23-2-2-211111133-2-2−3−5i32−3+5i3211−3−5i32−3−5i32−3+5i32−3+5i321111000000000000000088-4-4-2-23-2-2-211111133-2-2−3−5i32−3+5i3211−3−5i32−3−5i32−3+5i32−3+5i3211110000000000000000
χ2888-4-4-2-23-2-2-211111133-2-2−3+5i32−3−5i3211−3+5i32−3+5i32−3−5i32−3−5i321111000000000000000088-4-4-2-23-2-2-211111133-2-2−3+5i32−3−5i3211−3+5i32−3+5i32−3−5i32−3−5i3211110000000000000000
χ2988-4-4-2-2-23-2-2111111-2-23311−3−5i32−3+5i321111−3−5i32−3−5i32−3+5i32−3+5i32000000000000000088-4-4-2-2-23-2-2111111-2-23311−3−5i32−3+5i321111−3−5i32−3−5i32−3+5i32−3+5i320000000000000000
χ3088-4-4-2-2-23-2-2111111-2-23311−3+5i32−3−5i321111−3+5i32−3+5i32−3−5i32−3−5i32000000000000000088-4-4-2-2-23-2-2111111-2-23311−3+5i32−3−5i321111−3+5i32−3+5i32−3−5i32−3−5i320000000000000000
χ318-48-48-2-2-2-418-2-4-4111111-2-2-2-21111111100000000000000008-48-48-2-2-2-418-2-4-4111111-2-2-2-2111111110000000000000000
χ328-48-4-28-2-21-4-2811-4-41111-2-2-2-21111111100000000000000008-48-4-28-2-21-4-2811-4-41111-2-2-2-2111111110000000000000000
χ338-48-4-2-23-211-2-21111−3−i152−3+i1521−i151+i1533-2-2−3−i152−3+i152−3−i152−3+i1521−i151+i151−i151+i1500000000000000008-48-4-2-23-211-2-21111−3−i152−3+i1521−i151+i1533-2-2−3−i152−3+i152−3−i152−3+i1521−i151+i151−i151+i150000000000000000
χ348-48-4-2-23-211-2-21111−3+i152−3−i1521+i151−i1533-2-2−3+i152−3−i152−3+i152−3−i1521+i151−i151+i151−i1500000000000000008-48-4-2-23-211-2-21111−3+i152−3−i1521+i151−i1533-2-2−3+i152−3−i152−3+i152−3−i1521+i151−i151+i151−i150000000000000000
χ358-48-4-2-2-2311-2-211111−i151+i15−3+i152−3−i152-2-2331−i151+i151−i151+i15−3+i152−3−i152−3+i152−3−i15200000000000000008-48-4-2-2-2311-2-211111−i151+i15−3+i152−3−i152-2-2331−i151+i151−i151+i15−3+i152−3−i152−3+i152−3−i1520000000000000000
χ368-48-4-2-2-2311-2-211111+i151−i15−3−i152−3+i152-2-2331+i151−i151+i151−i15−3−i152−3+i152−3−i152−3+i15200000000000000008-48-4-2-2-2311-2-211111+i151−i15−3−i152−3+i152-2-2331+i151−i151+i151−i15−3−i152−3+i152−3−i152−3+i1520000000000000000
χ378-4-428-2-2-2-41-4122−1−352−1+35211111111−1−352−1+352−1+352−1−352−1−352−1+352−1+352−1−35200000000000000008-4-428-2-2-2-41-4122−1−352−1+35211111111−1−352−1+352−1+352−1−352−1−352−1+352−1+352−1−3520000000000000000
χ388-4-428-2-2-2-41-4122−1+352−1−35211111111−1+352−1−352−1−352−1+352−1+352−1−352−1−352−1+35200000000000000008-4-428-2-2-2-41-4122−1+352−1−35211111111−1+352−1−352−1−352−1+352−1+352−1−352−1−352−1+3520000000000000000
χ398-4-42-28-2-21-41-4−1−352−1+3522211111111−1−352−1+352−1+352−1−352−1+352−1−352−1−352−1+35200000000000000008-4-42-28-2-21-41-4−1−352−1+3522211111111−1−352−1+352−1+352−1−352−1+352−1−352−1−352−1+3520000000000000000
χ408-4-42-28-2-21-41-4−1+352−1−3522211111111−1+352−1−352−1−352−1+352−1−352−1+352−1+352−1−35200000000000000008-4-42-28-2-21-41-4−1+352−1−3522211111111−1+352−1−352−1−352−1+352−1−352−1+352−1+352−1−3520000000000000000
χ418-4-42-2-23-21111−1−352−1+352−1−352−1+352−3−i152−3+i1521−i151+i15−3−5i32−3+5i3211ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−1+i152−1−i152−1+i152−1−i15200000000000000008-4-42-2-23-21111−1−352−1+352−1−352−1+352−3−i152−3+i1521−i151+i15−3−5i32−3+5i3211ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−1+i152−1−i152−1+i152−1−i1520000000000000000
χ428-4-42-2-23-21111−1−352−1+352−1−352−1+352−3+i152−3−i1521+i151−i15−3+5i32−3−5i3211−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−1−i152−1+i152−1−i152−1+i15200000000000000008-4-42-2-23-21111−1−352−1+352−1−352−1+352−3+i152−3−i1521+i151−i15−3+5i32−3−5i3211−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−1−i152−1+i152−1−i152−1+i1520000000000000000
χ438-4-42-2-23-21111−1+352−1−352−1+352−1−352−3−i152−3+i1521−i151+i15−3+5i32−3−5i3211−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58−1+i152−1−i152−1+i152−1−i15200000000000000008-4-42-2-23-21111−1+352−1−352−1+352−1−352−3−i152−3+i1521−i151+i15−3+5i32−3−5i3211−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58−1+i152−1−i152−1+i152−1−i1520000000000000000
χ448-4-42-2-23-21111−1+352−1−352−1+352−1−352−3+i152−3−i1521+i151−i15−3−5i32−3+5i3211ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−1−i152−1+i152−1−i152−1+i15200000000000000008-4-42-2-23-21111−1+352−1−352−1+352−1−352−3+i152−3−i1521+i151−i15−3−5i32−3+5i3211ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−1−i152−1+i152−1−i152−1+i1520000000000000000
χ458-4-42-2-2-231111−1−352−1+352−1+352−1−3521−i151+i15−3+i152−3−i15211−3−5i32−3+5i32−1+i152−1−i152−1+i152−1−i152ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ4600000000000000008-4-42-2-2-231111−1−352−1+352−1+352−1−3521−i151+i15−3+i152−3−i15211−3−5i32−3+5i32−1+i152−1−i152−1+i152−1−i152ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ460000000000000000
χ468-4-42-2-2-231111−1−352−1+352−1+352−1−3521+i151−i15−3−i152−3+i15211−3+5i32−3−5i32−1−i152−1+i152−1−i152−1+i152−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ5800000000000000008-4-42-2-2-231111−1−352−1+352−1+352−1−3521+i151−i15−3−i152−3+i15211−3+5i32−3−5i32−1−i152−1+i152−1−i152−1+i152−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ58ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ580000000000000000
χ478-4-42-2-2-231111−1+352−1−352−1−352−1+3521−i151+i15−3+i152−3−i15211−3+5i32−3−5i32−1+i152−1−i152−1+i152−1−i152−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ5800000000000000008-4-42-2-2-231111−1+352−1−352−1−352−1+3521−i151+i15−3+i152−3−i15211−3+5i32−3−5i32−1+i152−1−i152−1+i152−1−i152−ζ2−3ζ14+ζ22−3ζ26−ζ38+ζ58−3ζ2−ζ14−ζ26+ζ34−3ζ38+ζ46ζ14−3ζ22+ζ26−ζ34−ζ46−3ζ58ζ2−ζ22−3ζ34+ζ38−3ζ46−ζ580000000000000000
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χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ501111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1
χ51111111111111111111111111111111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11111
χ52111111111111111111111111111111111-1-111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-111
χ5311111111111111111111111111111111-11-1-1-1i−ii−i-1i−ii−i1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111−ii−ii1−ii−ii-11
χ5411111111111111111111111111111111-11-1-1-1−ii−ii-1−ii−ii1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111i−ii−i1i−ii−i-11
χ5511111111111111111111111111111111-1-11-1-1i−i−ii-1i−i−ii-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111−iii−i1−iii−i1-1
χ5611111111111111111111111111111111-1-11-1-1−iii−i-1−iii−i-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111i−i−ii1i−i−ii1-1
χ5722-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12002-10022-100-1-100-2-211-2-2-2-2-2-2111111-2-2-2-2111111111111-200-2100-2-21001100
χ5822-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12002-100-2-2-1001100-2-211-2-2-2-2-2-2111111-2-2-2-2111111111111-200-210022100-1-100
χ5922-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-200-21002i−2i100−ii00-2-211-2-2-2-2-2-2111111-2-2-2-21111111111112002-100−2i2i-100i−i00
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χ612-12-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-122200-1-1-10000-21-21-2-2-2-211-2-211111111-2-2-2-211111111-2001-2-2-2001110000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.