Finite Group DatabasebetaFinite Group Databasebeta| order | 24353 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C49×C71 ⋊ C7 |
| Sylow | C71 ⋊ 7−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C7 | C7×C71⋊C7 |
| commutator, socle, cosocle | C7×C71 | C72 |
| Fitting | C49×C71 | C7 |
| prime radical | C7×C71⋊C7 | C7 |
| hypercenter | C49 | C71⋊C7 |
| hypocenter | C71 | 7−1+2 |
| LCS | G ▷ C7×C71 ▷ C71 | |
| UCS | C1 ◁ C7 ◁ C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3479 |
Polycyclic presentation:
7^3,71|a^7=c,b^a=bc,d^b=d^30545 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24353, 15);