Finite Group DatabasebetaFinite Group Databasebeta| order | 38130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽32)⋊D41) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊D123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C31×C41 | C2×C5 |
| LCS | G ▷ C3×C31×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 3813 |
A minimal faithful permutation representation — 2 generators on 75 points:
(2,3)(5,9,10,21,8,6,7,14,15,12)(11,26,27,28,13,17,18,30,32,20)(16,33,25,31,19,23,24,34,22,29)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75);(1,2,3)(4,5,8,13,15,22,32,26,10,16,25,33,27,29,17,9,7,11,19,30,24,34,23,14,18,28,31,21,20,12,6)(35,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37)Polycyclic presentation:
2,3,5,31,41|b^a=b^2,d^a=d^30,e^a=e^40,d^c=d^16684 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38130, 67);