Finite Group DatabasebetaFinite Group Databasebeta| order | 25281 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C53 |
No aliases for this group.
| derived, Sylow | C532 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C532⋊C3 |
| commutator, hypocenter | C532 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C532 | C3 |
| LCS | G ▷ C532 | |
| UCS | C1 ◁ C3 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 477 |
Polycyclic presentation:
3,53^2,3|a^3=d,b^a=b^31c^24,c^a=b^5c^212817 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25281, 4);