Finite Group DatabasebetaFinite Group Databasebeta| order | 24535 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C701⋊C5)⋊C7 |
| unambiguous semidirect product | (C701⋊C7)⋊C5 |
| Fitting, socle, derived, Sylow | C701 ⋊ C5×C7 |
| Hall | C701⋊C7 ⋊ C5 |
| Hall | C701⋊C5 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C701 | C5×C7 |
| LCS | G ▷ C701 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 701 |
Polycyclic presentation:
5,7,701|c^a=c^210,c^b=c^1955 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24535, 1);