Finite Group DatabasebetaFinite Group Databasebeta| order | 30394 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C167 · Schur multiplier (H2) = C1 |
| direct product | C167×D91 |
| unambiguous semidirect product | C7⋊(D13×C167) |
| unambiguous semidirect product | C13⋊(D7×C167) |
| Fitting, socle, Hall | C7×C13×C167 ⋊ C2 |
| derived, Hall | C7×C13 ⋊ C2×C167 |
| Hall | C13×C167 ⋊ D7 |
| Hall | C7×C167 ⋊ D13 |
| Sylow | C13 ⋊ D7×C167 |
| Sylow | C7 ⋊ D13×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | D91 |
| commutator, cosocle, hypocenter | C7×C13 | C2×C167 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C167 | C2 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C167 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15197 |
7849 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30394, 7);