Finite Group DatabasebetaFinite Group Databasebeta| order | 2170 |
| isoclinism | isoclinic class of C7⋊(D31⋊C5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D31⋊C5) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊D7 |
| unambiguous semidirect product | D217⋊C5 |
| Fitting, socle, derived, Hall | C7×C31 ⋊ C2×C5 |
| Hall | C7×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D217 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ D7 |
| Sylow | C31 ⋊ C5×D7 |
| Sylow | C7 ⋊ D31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C31 | C2×C5 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 217 |
Polycyclic presentation:
2,5,7,31|c^a=c^6,d^a=d^30,d^b=d^1646 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, 12);