Finite Group DatabasebetaFinite Group Databasebeta| order | 30861 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C310 |
| direct product | C34×C127⋊C3 |
| unambiguous semidirect product | C127⋊C35 |
| unambiguous semidirect product | (C3×C127)⋊C34 |
| Fitting, socle | C34×C127 ⋊ C3 |
| derived, Sylow | C127 ⋊ C35 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C34 | C127⋊C3 |
| commutator, cosocle, hypocenter | C127 | C35 |
| Frattini | C1 | G |
| Fitting, socle | C34×C127 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C34 | |
5328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10287 |
3645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30861, 309);