Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (#64418⋊C3)⋊D19 |
| Fitting, socle, Hall | C72×C19 ⋊ C2×C3×D3 |
| derived | C19×#3862 ⋊ C22×C3 |
| Hall | C19×ΓL(1,𝔽8)2 ⋊ C22 |
| Hall | ΓL(1,𝔽8)2 ⋊ C2×D19 |
| Sylow | C72 ⋊ C3×D3×D19 |
| Sylow | C19 ⋊ (#64418⋊C2)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C19×#3862 | C22×C3 |
| Fitting, socle | C72×C19 | C2×C3×D3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 | |
152 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 266 |
Polycyclic presentation:
2^2,3^2,19,7^2|d^a=d^2,e^a=e^18,f^a=f^2g^3,g^a=f^6g^5,d^b=d^2,f^b=f^5g^4,g^b=fg^2,f^c=f^4,g^c=g^4,f^d=f^4g^4,g^d=g^2205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 805);