Finite Group DatabasebetaFinite Group Databasebeta| order | 30129 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C83 · Schur multiplier (H2) = C11 |
| direct product | C83×C112⋊C3 |
| unambiguous semidirect product | C112⋊(C3×C83) |
| unambiguous semidirect product | (C112×C83)⋊C3 |
| Fitting, socle, Hall | C112×C83 ⋊ C3 |
| derived, Sylow | C112 ⋊ C3×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | C112⋊C3 |
| commutator, cosocle, hypocenter | C112 | C3×C83 |
| Frattini | C1 | G |
| Fitting, socle | C112×C83 | C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C83 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2739 |
3569 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30129, 3);