Finite Group DatabasebetaFinite Group Databasebeta| order | 24353 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C72 |
| unambiguous semidirect product | C72⋊(C71⋊C7) |
| unambiguous semidirect product | C71⋊H(3,𝔽7) |
| unambiguous semidirect product | (C7×C71⋊C7)⋊C7 |
| Fitting | C72×C71 ⋊ C7 |
| Sylow | C71 ⋊ H(3,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C7 | C7×C71⋊C7 |
| commutator, socle, cosocle | C7×C71 | C72 |
| Fitting | C72×C71 | C7 |
| hypercenter | C72 | C71⋊C7 |
| hypocenter | C71 | H(3,𝔽7) |
| LCS | G ▷ C7×C71 ▷ C71 | |
| UCS | C1 ◁ C7 ◁ C72 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3479 |
Polycyclic presentation:
7^3,71|b^a=bc,d^b=d^45545 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24353, 9);