Finite Group DatabasebetaFinite Group Databasebeta| order | 29610 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D1645 |
| unambiguous semidirect product | C5⋊(C32×D329) |
| unambiguous semidirect product | C47⋊(C32×D35) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D1645 |
| commutator, cosocle, hypocenter | C5×C7×C47 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C47 | C2 |
| LCS | G ▷ C5×C7×C47 | |
| UCS | C1 ◁ C32 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14805 |
7416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29610, 48);