Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C52×C13 ⋊ C4 |
| Hall | C52×C13 ⋊ #157 |
| Hall | C32×C52 ⋊ Dic13 |
| Hall | C32×C13 ⋊ #1039 |
| Sylow | C52 ⋊ #90865 |
| Sylow | C13 ⋊ #11744710 |
| Sylow | C32 ⋊ #13049918 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52×C13 | C4 |
| prime radical, cosocle | C52×C13×C3⋊D3 | C2 |
| LCS | G ▷ C32×C52×C13 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5^2,13|a^2=b,c^a=cd,d^a=cd^2,e^a=e^4,f^a=f^4,g^a=g^12,c^b=c^2,d^b=d^2978 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 706);