Finite Group DatabasebetaFinite Group Databasebeta| order | 2170 |
| isoclinism | isoclinic class of D31⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D31⋊C5 |
| unambiguous semidirect product | D31⋊(C5×C7) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D31)⋊C5 |
| Fitting, socle, Hall | C7×C31 ⋊ C2×C5 |
| derived, Sylow | C31 ⋊ C2×C5×C7 |
| Hall | C7×ΓL(1,𝔽32) ⋊ C2 |
| Hall | C7×D31 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×C7 |
| Hall | D31 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D31⋊C5 |
| commutator, cosocle, hypocenter | C31 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C31 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 217 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,2,3,4,5,6,7)(9,13,14,25,12,10,11,18,19,16)(15,30,31,32,17,21,22,34,36,24)(20,37,29,35,23,27,28,38,26,33);(8,9,12,17,19,26,36,30,14,20,29,37,31,33,21,13,11,15,23,34,28,38,27,18,22,32,35,25,24,16,10)91 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D31⋊C5, C2×C7×D31⋊C5, C5×C7×D31⋊C5, … |
| maximal normal subgroup of | D7×D31⋊C5, C2×C7×D31⋊C5, C5×C7×D31⋊C5, … |
| maximal quotient of | C7×Dic31⋊C5, C2×C7×D31⋊C5, C7×D31⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2170, 10);