Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Hall | C72×C19 ⋊ C4×C9 |
| Hall | #22552721 ⋊ C4 |
| Hall | C72×Dic19 ⋊ C9 |
| Hall | Dic19 ⋊ #89205 |
| Sylow | C72 ⋊ #4296⋊C4 |
| Sylow | C19 ⋊ C4×#89205 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #30660708 |
| commutator, hypocenter | C72×C19 | C4×C9 |
| Fitting, socle | C2×C72×C19 | C2×C9 |
| prime radical, cosocle | C2×C72×C19⋊C3 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1596 |
Polycyclic presentation:
2,3^2,7^2,19,2|a^2=g,b^3=c,f^a=f^18,d^b=d^2,e^b=e^4,f^b=f^4,f^c=f^7326 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 590);