Finite Group DatabasebetaFinite Group Databasebeta| order | 25020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C3×C5×C139 ⋊ C2×C3 |
| derived | C3×C139 ⋊ C22×C3×C5 |
| Hall | C3×C5×C139⋊C3 ⋊ C22 |
| Hall | C3×C139⋊C3 ⋊ C22×C5 |
| Hall | C5×C139 ⋊ C2×C3×D3 |
| Sylow | C139 ⋊ C2×C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C3⋊(D139⋊C3) |
| commutator, cosocle, hypocenter | C3×C139 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C139 | C2×C3 |
| LCS | G ▷ C3×C139 | |
| UCS | C1 ◁ C2×C5 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 4170 |
A minimal faithful permutation representation — 2 generators on 149 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,99,72,73,123)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,110,102,83,84,86)(63,114,108,87,88,81)(74,115,116,101,89,133)(76,125,126,103,100,121)(79,94,124,105,106,122)(85,129,128,111,112,118)(92,136,107,119,120,109)(104,134,135,127,117,138)(113,139,132,130,131,137)(141,142)(143,144,145,146,147);(1,2,5,11,19,32,51,74,102,68,28,43,44,27,42,63,89,117,131,135,99,124,136,133,129,125,98,119,78,31,48,59,62,64,90,118,127,103,75,52,33,20,4,8,13,23,37,56,79,107,108,80,45,15,26,14,25,40,60,85,113,132,126,70,95,114,110,96,69,94,106,50,71,84,88,91,93,121,137,130,111,83,58,36,10,16,24,38,57,81,109,105,77,54,35,22,7,6,12,21,34,53,76,104,128,97,47,66,82,67,46,65,92,73,100,112,116,120,122,123,138,139,134,115,87,55,18,29,39,41,61,86,101,72,49,30,17,9,3)(140,141,142)(148,149)780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25020, 77);