Finite Group DatabasebetaFinite Group Databasebeta| order | 22625 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C25×C181 ⋊ C5 |
| Sylow | C181 ⋊ 5−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C5×C181⋊C5 |
| commutator, socle, cosocle | C5×C181 | C52 |
| Fitting | C25×C181 | C5 |
| prime radical | C5×C181⋊C5 | C5 |
| hypercenter | C25 | C181⋊C5 |
| hypocenter | C181 | 5−1+2 |
| LCS | G ▷ C5×C181 ▷ C181 | |
| UCS | C1 ◁ C5 ◁ C25 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4525 |
Polycyclic presentation:
5^3,181|a^5=c,b^a=bc,d^b=d^135929 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22625, 13);