Finite Group DatabasebetaFinite Group Databasebeta| order | 29524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C112 · Schur multiplier (H2) = C2×C11 |
| direct product | C2×C112×D61 |
| unambiguous semidirect product | C61⋊(C22×C112) |
| unambiguous semidirect product | (C2×C61)⋊(C2×C112) |
| Fitting, socle | C2×C112×C61 ⋊ C2 |
| derived, Sylow | C61 ⋊ C22×C112 |
| Hall | C112×C61 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C112 | D61 |
| commutator, cosocle, hypocenter | C61 | C22×C112 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C61 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C112 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14762 |
7744 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29524, 30);