Finite Group DatabasebetaFinite Group Databasebeta| order | 30951 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#13108658 |
| Fitting, socle, Hall | C19×C181 ⋊ C9 |
| derived, Sylow | C181 ⋊ C9×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #13108658 |
| commutator, hypocenter | C181 | C9×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C181 | C9 |
| prime radical | C19×C181⋊C3 | C3 |
| cosocle | C181⋊C3 | C3×C19 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C19 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3439 |
551 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30951, 7);