Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C72×C19 ⋊ C3×Dic3 |
| derived | C19×#3862 ⋊ C3×C4 |
| Hall | C19×ΓL(1,𝔽8)2 ⋊ C4 |
| Hall | ΓL(1,𝔽8)2 ⋊ Dic19 |
| Sylow | C72 ⋊ C3×Dic57 |
| Sylow | C19 ⋊ #10596885⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C19×#3862 | C3×C4 |
| Fitting, socle | C72×C19 | C3×Dic3 |
| prime radical | C19×ΓL(1,𝔽8)⋊AGL(1,𝔽7) | C2 |
| cosocle | C19×#64425 | C2×C3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
Polycyclic presentation:
2,3,2,3,19,7^2|a^2=c,d^a=d^2,e^a=e^18,f^a=f^5g^2,g^a=fg^2,f^b=f^4,g^b=g^4,f^c=f^6,g^c=g^6,f^d=f^4g^4,g^d=g^2256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 797);