Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| isoclinism | isoclinic class of C3⋊(C3⋊#261) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C52×C3⋊(C3⋊#261) |
| unambiguous semidirect product | C3⋊(C52×C3⋊#261) |
| Fitting, socle, Hall | C32×C52×C13 ⋊ C4 |
| derived, Hall | C32×C13 ⋊ C4×C52 |
| Hall | C52×C13 ⋊ C3⋊Dic3 |
| Hall | C32×C52 ⋊ #261 |
| Sylow | C13 ⋊ C52×C3⋊Dic3 |
| Sylow | C32 ⋊ C52×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C3⋊(C3⋊#261) |
| commutator, hypocenter | C32×C13 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C13 | C4 |
| prime radical | C32×C52×D13 | C2 |
| cosocle | C32×D13 | C2×C52 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C52 | |
288 conjugacy classes of subgroups.
975 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 623);