Finite Group DatabasebetaFinite Group Databasebeta| order | 25011 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C397 ⋊ C9 |
| Sylow | C397 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ #16813210 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C397 | C9 |
| prime radical, cosocle | C7×C397⋊C3 | C3 |
| LCS | G ▷ C7×C397 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2779 |
Polycyclic presentation:
3^2,7,397|a^3=b,c^a=c^2,d^a=d^312,d^b=d^34323 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25011, 8);