Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5 |
| direct product | C2×C3×(C5⋊D5)⋊(C13⋊C3) |
| unambiguous semidirect product | (C2×C3×C5⋊D5)⋊(C13⋊C3) |
| Fitting, socle | C2×C3×C52×C13 ⋊ C2×C3 |
| derived, Hall | C52×C13 ⋊ C22×C32 |
| Hall | C3×C13⋊(C52⋊C3) ⋊ C22 |
| Hall | C2×C13×C5⋊D5 ⋊ C32 |
| Hall | C2×C5⋊D5 ⋊ C3×C13⋊C3 |
| Sylow | C52 ⋊ C22×C3×C13⋊C3 |
| Sylow | C13 ⋊ C2×C3×(C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | (C5⋊D5)⋊(C13⋊C3) |
| commutator, cosocle, hypocenter | C52×C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C2×C3 | |
160 conjugacy classes of subgroups.
396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 544);