Finite Group DatabasebetaFinite Group Databasebeta| order | 29772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D827 |
| unambiguous semidirect product | C827⋊(C22×C32) |
| unambiguous semidirect product | (C2×C827)⋊(C2×C32) |
| Fitting, socle | C2×C32×C827 ⋊ C2 |
| derived, Sylow | C827 ⋊ C22×C32 |
| Hall | C32×C827 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D827 |
| commutator, cosocle, hypocenter | C827 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C827 | C2 |
| LCS | G ▷ C827 | |
| UCS | C1 ◁ C2×C32 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14886 |
7470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29772, 26);