Finite Group DatabasebetaFinite Group Databasebeta| order | 16870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×C241⋊C5 |
| unambiguous semidirect product | (C2×C241)⋊(C5×C7) |
| unambiguous semidirect product | (C2×C7×C241)⋊C5 |
| Fitting, socle, Hall | C2×C7×C241 ⋊ C5 |
| derived, Sylow | C241 ⋊ C2×C5×C7 |
| Hall | C7×C241 ⋊ C2×C5 |
| Hall | C2×C241 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C241⋊C5 |
| commutator, cosocle, hypocenter | C241 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C241 | C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C2×C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3374 |
742 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C7×C241⋊C5, C7×Dic241⋊C5, Dic7×C241⋊C5, … |
| maximal normal subgroup of | C4×C7×C241⋊C5, C7×Dic241⋊C5, Dic7×C241⋊C5, … |
| maximal quotient of | C4×C7×C241⋊C5, C22×C7×C241⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16870, 2);