Finite Group DatabasebetaFinite Group Databasebeta| order | 24185 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C691⋊C5 |
| unambiguous semidirect product | C691⋊(C5×C7) |
| unambiguous semidirect product | (C7×C691)⋊C5 |
| Fitting, socle, Hall | C7×C691 ⋊ C5 |
| derived, Sylow | C691 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C691⋊C5 |
| commutator, cosocle, hypocenter | C691 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C691 | C5 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4837 |
1001 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24185, 1);