Finite Group DatabasebetaFinite Group Databasebeta| order | 15600 |
| isoclinism | isoclinic class of SL(2,𝔽25) |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C1 |
| special linear | SL(2,𝔽25) |
| symplectic | Sp(2,𝔽25) |
| special unitary | SU(2,𝔽25) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, cosocle, hypercenter | C2 | PSL(2,𝔽25) |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
Permutation generators:
(4,12,29,32,13)(5,15,35,38,16)(7,20,45,48,21)(8,23,51,54,24)(10,25,57,60,26)(11,27,63,66,28)(18,41,71,82,42)(19,43,72,81,44)(30,73,155,110,74)(31,76,105,164,77)(33,83,112,173,84)(34,86,177,107,87)(36,91,183,106,92)(37,94,109,184,95)(39,99,108,187,100)(40,102,188,111,103)(46,114,139,59,115)(47,117,64,146,118)(49,120,62,143,121)(50,123,150,67,124)(52,126,147,65,127)(53,129,58,138,130)(55,132,68,151,133)(56,135,142,61,136)(69,116,193,191,153)(70,154,194,202,144)(75,161,159,174,104)(78,168,171,166,101)(79,169,200,198,122)(80,140,189,204,170)(85,96,156,172,167)(88,93,165,160,180)(89,128,196,192,181)(90,182,195,201,152)(97,185,199,197,134)(98,148,190,203,186)(113,137,205,162,176)(119,157,179,206,141)(125,145,207,163,175)(131,158,178,208,149);(1,2,6,17,14,22,9,3)(4,10,19,8,5,11,18,7)(12,30,75,51,125,108,42,107,141,60,96,37,15,36,93,45,113,112,44,111,149,66,78,31)(13,33,85,54,131,106,41,105,137,57,104,40,16,39,101,48,119,110,43,109,145,63,88,34)(20,46,116,72,152,68,28,67,80,32,79,53,23,52,128,71,144,62,26,61,98,38,97,47)(21,49,122,81,148,65,27,64,70,29,69,56,24,55,134,82,140,59,25,58,90,35,89,50)(73,156,195,207,183,124,177,176,200,167,102,127,91,168,194,205,155,136,188,175,199,166,86,115)(74,138,190,163,196,118,87,121,153,172,186,151,92,146,189,162,193,130,103,133,181,171,170,143)(76,114,169,159,182,147,99,150,202,179,198,135,94,126,185,160,154,139,83,142,201,178,197,123)(77,120,84,174,203,208,187,117,164,157,191,161,95,132,100,180,204,206,173,129,184,158,192,165);(1,4,14,5)(2,7,22,8)(3,10,17,11)(6,18,9,19)(12,16,15,13)(20,24,23,21)(25,28,27,26)(29,71,35,72)(30,40,36,34)(31,39,37,33)(32,81,38,82)(41,44,43,42)(45,63,51,57)(46,56,52,50)(47,55,53,49)(48,60,54,66)(58,68,64,62)(59,67,65,61)(69,128,89,116)(70,144,90,152)(73,157,91,158)(74,159,92,160)(75,104,93,88)(76,162,94,163)(77,166,95,167)(78,101,96,85)(79,122,97,134)(80,148,98,140)(83,171,99,172)(84,175,100,176)(86,161,102,165)(87,178,103,179)(105,112,109,108)(106,111,110,107)(113,145,125,137)(114,189,126,190)(115,191,127,192)(117,194,129,195)(118,197,130,198)(119,141,131,149)(120,199,132,200)(121,201,133,202)(123,193,135,196)(124,203,136,204)(138,169,146,185)(139,170,147,186)(142,181,150,153)(143,182,151,154)(155,206,183,208)(156,164,168,184)(173,207,187,205)(174,188,180,177)29 conjugacy classes — view the full character table.
| maximal subgroup of | ΣL(2,𝔽25) |
| maximal normal subgroup of | ΣL(2,𝔽25) |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((4,12,29,32,13)(5,15,35,38,16)(7,20,45,48,21)(8,23,51,54,24)(10,25,57,60,26)(11,27,63,66,28)(18,41,71,82,42)(19,43,72,81,44)(30,73,155,110,74)(31,76,105,164,77)(33,83,112,173,84)(34,86,177,107,87)(36,91,183,106,92)(37,94,109,184,95)(39,99,108,187,100)(40,102,188,111,103)(46,114,139,59,115)(47,117,64,146,118)(49,120,62,143,121)(50,123,150,67,124)(52,126,147,65,127)(53,129,58,138,130)(55,132,68,151,133)(56,135,142,61,136)(69,116,193,191,153)(70,154,194,202,144)(75,161,159,174,104)(78,168,171,166,101)(79,169,200,198,122)(80,140,189,204,170)(85,96,156,172,167)(88,93,165,160,180)(89,128,196,192,181)(90,182,195,201,152)(97,185,199,197,134)(98,148,190,203,186)(113,137,205,162,176)(119,157,179,206,141)(125,145,207,163,175)(131,158,178,208,149), (1,2,6,17,14,22,9,3)(4,10,19,8,5,11,18,7)(12,30,75,51,125,108,42,107,141,60,96,37,15,36,93,45,113,112,44,111,149,66,78,31)(13,33,85,54,131,106,41,105,137,57,104,40,16,39,101,48,119,110,43,109,145,63,88,34)(20,46,116,72,152,68,28,67,80,32,79,53,23,52,128,71,144,62,26,61,98,38,97,47)(21,49,122,81,148,65,27,64,70,29,69,56,24,55,134,82,140,59,25,58,90,35,89,50)(73,156,195,207,183,124,177,176,200,167,102,127,91,168,194,205,155,136,188,175,199,166,86,115)(74,138,190,163,196,118,87,121,153,172,186,151,92,146,189,162,193,130,103,133,181,171,170,143)(76,114,169,159,182,147,99,150,202,179,198,135,94,126,185,160,154,139,83,142,201,178,197,123)(77,120,84,174,203,208,187,117,164,157,191,161,95,132,100,180,204,206,173,129,184,158,192,165), (1,4,14,5)(2,7,22,8)(3,10,17,11)(6,18,9,19)(12,16,15,13)(20,24,23,21)(25,28,27,26)(29,71,35,72)(30,40,36,34)(31,39,37,33)(32,81,38,82)(41,44,43,42)(45,63,51,57)(46,56,52,50)(47,55,53,49)(48,60,54,66)(58,68,64,62)(59,67,65,61)(69,128,89,116)(70,144,90,152)(73,157,91,158)(74,159,92,160)(75,104,93,88)(76,162,94,163)(77,166,95,167)(78,101,96,85)(79,122,97,134)(80,148,98,140)(83,171,99,172)(84,175,100,176)(86,161,102,165)(87,178,103,179)(105,112,109,108)(106,111,110,107)(113,145,125,137)(114,189,126,190)(115,191,127,192)(117,194,129,195)(118,197,130,198)(119,141,131,149)(120,199,132,200)(121,201,133,202)(123,193,135,196)(124,203,136,204)(138,169,146,185)(139,170,147,186)(142,181,150,153)(143,182,151,154)(155,206,183,208)(156,164,168,184)(173,207,187,205)(174,188,180,177));