Finite Group DatabasebetaFinite Group Databasebeta| order | 24525 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊#11758279 |
| derived, Hall | C52×C109 ⋊ C9 |
| Sylow | C109 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ #11758279 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C52⋊(C109⋊C3) |
| commutator, hypocenter | C52×C109 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C52×C109 | C3 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4905 |
Polycyclic presentation:
3,5^2,109,3|a^3=e,b^a=bc^3,c^a=b^4c^3,d^a=d^632733 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24525, 7);