Finite Group DatabasebetaFinite Group Databasebeta| order | 16900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#10621728 |
| Fitting, Hall | C132×C25 ⋊ C4 |
| derived, Sylow | C132 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #10621728 |
| commutator, hypocenter | C132 | C4×C25 |
| Frattini | C5 | C5×#10621728 |
| Fitting | C132×C25 | C4 |
| socle | C5×C132 | C4×C5 |
| prime radical, cosocle | C5×C13⋊D13 | C2×C5 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C25 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4225 |
1150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16900, 59);