Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| direct product | #1039×C13⋊C9 |
| derived, Hall | C52×C13 ⋊ C4×C9 |
| Hall | C52×C13⋊C9 ⋊ C4 |
| Hall | C13×#1039 ⋊ C9 |
| Sylow | C52 ⋊ C4×C13⋊C9 |
| Sylow | C13 ⋊ C9×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C13⋊C3×C5⋊D5 |
| commutator, hypocenter | C52×C13 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C52×C13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C2×C3 | |
144 conjugacy classes of subgroups.
588 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 79);