Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C19 ⋊ C22×C9 |
| Hall | #22552721 ⋊ C22 |
| Hall | D72×C19 ⋊ C9 |
| Hall | D72 ⋊ #4296 |
| Sylow | C72 ⋊ C22×#4296 |
| Sylow | C19 ⋊ #11725075⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C22×C9 |
| prime radical | D72×C19⋊C3 | C3 |
| cosocle | C72×C19⋊C3 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
128 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 798 |
Polycyclic presentation:
2^2,3^2,7^2,19|c^3=d,e^a=e^6,f^b=f^6,e^c=e^2,f^c=f^4,g^c=g^4,g^d=g^7107 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 889);