Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic1197 |
| unambiguous semidirect product | C9⋊(C7⋊Dic133) |
| unambiguous semidirect product | C19⋊(C7⋊Dic63) |
| derived, Hall | C72×C9×C19 ⋊ C4 |
| Hall | C72×C19 ⋊ Dic9 |
| Hall | C72×C9 ⋊ Dic19 |
| Hall | C9×C19 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic171 |
| Sylow | C19 ⋊ C7⋊Dic63 |
| Sylow | C9 ⋊ C7⋊Dic133 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊D1197 |
| commutator, hypocenter | C72×C9×C19 | C4 |
| Frattini | C2×C3 | C3⋊(C7⋊D133) |
| Fitting, cosocle | C2×C72×C9×C19 | C2 |
| socle, prime radical | C2×C3×C72×C19 | D3 |
| LCS | G ▷ C72×C9×C19 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33516 |
Polycyclic presentation:
2,3,7^2,19,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^6,d^a=d^6,e^a=e^18,g^a=g^28382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 335);