Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| isoclinism | isoclinic class of #90866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C3 |
| direct product | C25×#90866 |
| Fitting, Hall | C32×C13×C25 ⋊ C4 |
| derived, Hall | C32×C13 ⋊ C4×C25 |
| Hall | C13×C25 ⋊ #157 |
| Hall | C32×C25 ⋊ #261 |
| Sylow | C13 ⋊ C25×#157 |
| Sylow | C32 ⋊ C25×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #90866 |
| commutator, hypocenter | C32×C13 | C4×C25 |
| Frattini | C5 | C5×#90866 |
| Fitting | C32×C13×C25 | C4 |
| socle | C32×C5×C13 | C4×C5 |
| prime radical, cosocle | C5×C3⋊D39 | C2×C5 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C25 | |
60 conjugacy classes of subgroups.
825 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 171);