Finite Group DatabasebetaFinite Group Databasebeta| order | 24353 |
| automorphism | ? |
| homology | Abelianization (H1) = C73 · Schur multiplier (H2) = C73 |
| direct product | C72×C71⋊C7 |
| unambiguous semidirect product | C71⋊C73 |
| unambiguous semidirect product | (C7×C71)⋊C72 |
| Fitting, socle | C72×C71 ⋊ C7 |
| derived, Sylow | C71 ⋊ C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C71⋊C7 |
| commutator, cosocle, hypocenter | C71 | C73 |
| Frattini | C1 | G |
| Fitting, socle | C72×C71 | C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C72 | |
232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3479 |
833 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24353, 17);