Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊((C19⋊C3)⋊(C7⋊Dic7)) |
| unambiguous semidirect product | (C19⋊C3)⋊(C3⋊(C7⋊Dic7)) |
| derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×C72×C19⋊C3 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ C3×C3⋊(C7⋊Dic7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊((C19⋊C3)⋊(C7⋊D7)) |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×C72×C19⋊C3 | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11172 |
Polycyclic presentation:
2,3^2,7^2,19,2|a^2=g,c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^18,f^b=f^71332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 744);