Finite Group DatabasebetaFinite Group Databasebeta| order | 24206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D247 |
| unambiguous semidirect product | C13⋊(C72×D19) |
| unambiguous semidirect product | C19⋊(C72×D13) |
| Fitting, socle, Hall | C72×C13×C19 ⋊ C2 |
| derived, Hall | C13×C19 ⋊ C2×C72 |
| Hall | C72×C19 ⋊ D13 |
| Hall | C72×C13 ⋊ D19 |
| Sylow | C19 ⋊ C72×D13 |
| Sylow | C13 ⋊ C72×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D247 |
| commutator, cosocle, hypocenter | C13×C19 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13×C19 | C2 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C72 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12103 |
6125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24206, 12);