Finite Group DatabasebetaFinite Group Databasebeta| order | 11700 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #16839082⋊C3 |
| unambiguous semidirect product | #16839104⋊C3 |
| unambiguous semidirect product | #16839106⋊C3 |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C32×C4 |
| Hall | C13⋊C3×C52⋊C3 ⋊ C4 |
| Hall | #13049927 ⋊ C32 |
| Sylow | C52 ⋊ C3×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×#1043⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C13 | C32×C4 |
| prime radical | (C13⋊C3)⋊((C5⋊D5)⋊C3) | C2 |
| cosocle | C5⋊D65 | C2×C32 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,2,5^2,13|a^2=d,e^a=e^3,f^a=f^3,g^a=g^5,g^b=g^3,e^c=ef,f^c=e^2f^3,e^d=e^4,f^d=f^4,g^d=g^1253 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11700, 392);