Finite Group DatabasebetaFinite Group Databasebeta| order | 24353 |
| automorphism | ? |
| homology | Abelianization (H1) = C343 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊C343 |
| derived, Sylow | C71 ⋊ C343 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C49 | C71⋊C7 |
| commutator, hypocenter | C71 | C343 |
| Fitting, cosocle | C49×C71 | C7 |
| socle, prime radical | C7×C71 | C49 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C49 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24353 |
Polycyclic presentation:
7^3,71|a^7=b,b^7=c,d^a=d^45833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24353, 6);