Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived | C3×C72×C19 ⋊ C22×C3 |
| Hall | C3×C19⋊#3862 ⋊ C22 |
| Hall | C72×C19 ⋊ C2×C3×D3 |
| Sylow | C72 ⋊ D3×D19⋊C3 |
| Sylow | C19 ⋊ C2×C3⋊#64422 |
| 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 39 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 2394 |
A minimal faithful permutation representation — 2 generators on 36 points:
(2,3)(5,6,7)(8,10,9)(12,16,15,13,14,17)(18,19,25)(20,29,33)(21,23,30)(22,32,24)(26,35,31)(27,34,36);(1,2,3)(4,5,6,8,7,9,10)(11,12,15,16,14,17,13)(19,20)(21,23)(22,26)(24,25)(27,31)(28,33)(29,35)(30,36)(32,34)Polycyclic presentation:
2^2,3^2,7^2,19|g^a=g^18,d^b=d^2,f^b=f^6,e^c=e^2,f^c=f^4,g^c=g^7324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 1233);