Finite Group DatabasebetaFinite Group Databasebeta| order | 38130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#27163275 |
| 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)(36,40,41,55,60,37,38,46,48,70)(39,51,52,47,73,43,44,65,57,58)(42,54,53,64,75,45,50,66,67,69)(49,72,56,74,59,62,63,71,61,68);(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)(35,36,39,45,40,47,59,66,51,65,60,75,50,64,63,71,41,49,48,61,73,58,74,55,62,46,56,72,67,54,69,70,52,44,53,68,57,38,42,43,37)Polycyclic presentation:
2,3,5,31,41|b^a=b^2,d^a=d^30,e^a=e^40,d^c=d^16,e^c=e^37396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38130, 71);