Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×#16839092 |
| Fitting, socle | C3×C52×C13 ⋊ C3×C4 |
| derived, Hall | C52×C13 ⋊ C32×C4 |
| Hall | C3×C52×C13⋊C3 ⋊ C4 |
| Hall | #13049937 ⋊ C32 |
| Hall | C3×C13⋊C3 ⋊ #1039 |
| Sylow | C52 ⋊ C3×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C32×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16839092 |
| commutator, hypocenter | C52×C13 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C13 | C3×C4 |
| prime radical | C3×C52×D13⋊C3 | C2 |
| cosocle | C52×D13 | C2×C32 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C3 | |
288 conjugacy classes of subgroups.
327 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 425);