Finite Group DatabasebetaFinite Group Databasebeta| order | 25205 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C71 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C712 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C712 | C5 |
| LCS | G ▷ C712 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 355 |
Polycyclic presentation:
5,71^2|b^a=b^54,c^a=c^251013 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25205, 6);