Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#13183527 |
| derived, Hall | C19×#89205 ⋊ C4 |
| Hall | C72×C19 ⋊ Dic9 |
| Hall | #89205 ⋊ Dic19 |
| Sylow | C72 ⋊ Dic171 |
| Sylow | C19 ⋊ #13183527 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊#11725071 |
| commutator, hypocenter | C19×#89205 | C4 |
| Frattini | C2×C3 | C19⋊#64418 |
| Fitting, socle, prime radical | C2×C3×C72×C19 | D3 |
| cosocle | C2×C19×#89205 | C2 |
| LCS | G ▷ C19×#89205 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4788 |
Polycyclic presentation:
2,3,19,7^2,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^18,d^a=d^2e^3,e^a=d^6e^5,g^a=g^2,d^b=d^4e^4,e^b=e^21104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 315);