Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊D19)⋊D21 |
| Fitting, socle, derived | C3×C72×C19 ⋊ C22×C3 |
| Hall | C3×C7×C19×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C72×C19 ⋊ C2×C3×D3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C2×D19 |
| Sylow | C72 ⋊ C3×D3×D19 |
| Sylow | C19 ⋊ AGL(1,𝔽7)×D21 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C19 | C22×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 | |
184 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2394 |
Polycyclic presentation:
2^2,3^2,7^2,19|d^a=d^2,e^a=e^6,g^a=g^18,d^b=d^2,e^b=e^6,f^b=f^6,f^c=f^2597 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 1139);