Finite Group DatabasebetaFinite Group Databasebeta| order | 30394 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2171 |
| unambiguous semidirect product | C13⋊(C7×D167) |
| unambiguous semidirect product | C167⋊(C7×D13) |
| Fitting, socle, Hall | C7×C13×C167 ⋊ C2 |
| derived, Hall | C13×C167 ⋊ C2×C7 |
| Hall | C7×C167 ⋊ D13 |
| Sylow | C167 ⋊ C7×D13 |
| Hall | C7×C13 ⋊ D167 |
| Sylow | C13 ⋊ C7×D167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2171 |
| commutator, cosocle, hypocenter | C13×C167 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C167 | C2 |
| LCS | G ▷ C13×C167 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15197 |
7609 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30394, 4);