Finite Group DatabasebetaFinite Group Databasebeta| order | 24843 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C169⋊C3 |
| unambiguous semidirect product | C169⋊(C3×C72) |
| Fitting, Hall | C72×C169 ⋊ C3 |
| derived, Sylow | C169 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C3×C72 |
| Frattini | C13 | C72×C13⋊C3 |
| Fitting | C72×C169 | C3 |
| socle | C72×C13 | C13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C72 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8281 |
2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24843, 7);