Finite Group DatabasebetaFinite Group Databasebeta| order | 24525 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5 |
| Fitting, socle | C3×C52×C109 ⋊ C3 |
| derived, Sylow | C109 ⋊ C32×C52 |
| Hall | C52×C109 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | C109⋊C3 |
| commutator, cosocle, hypocenter | C109 | C32×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C109 | C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C3×C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8175 |
2925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24525, 16);