Finite Group DatabasebetaFinite Group Databasebeta| order | 25281 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C53 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C532 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C532 | C9 |
| prime radical, cosocle | C532⋊C3 | C3 |
| LCS | G ▷ C532 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 477 |
Polycyclic presentation:
3^2,53^2|a^3=b,c^a=c^20d^18,d^a=c^44d^37,c^b=c^31d^5,d^b=c^24d^21321 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25281, 6);