Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #261⋊(C52⋊C9) |
| derived, Hall | C52×C13 ⋊ C4×C9 |
| Hall | C13⋊(C52⋊C9) ⋊ C4 |
| Hall | C52×#261 ⋊ C9 |
| Hall | #261 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ #261⋊C9 |
| 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.
Polycyclic presentation:
2,3,2,5^2,13,3|a^2=c,b^3=g,f^a=f^5,d^b=d^3e^2,e^b=de,f^b=f^3,f^c=f^12207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 238);