Finite Group DatabasebetaFinite Group Databasebeta| order | 30927 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#14558652 |
| Fitting, socle, Hall | C132×C61 ⋊ C3 |
| derived | C13×C61 ⋊ C3×C13 |
| Sylow | C132 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #14558652 |
| commutator, cosocle, hypocenter | C13×C61 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C132×C61 | C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2379 |
3471 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30927, 10);