Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| direct product | #261×C52⋊C9 |
| derived, Hall | C52×C13 ⋊ C4×C9 |
| Hall | C13×C52⋊C9 ⋊ C4 |
| Hall | C52×#261 ⋊ C9 |
| Sylow | C52 ⋊ C9×#261 |
| Sylow | C13 ⋊ C4×C52⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #261×C52⋊C3 |
| commutator, hypocenter | C52×C13 | C4×C9 |
| Fitting, socle | C3×C52×C13 | C3×C4 |
| prime radical, cosocle | C3×C52×D13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 239);