Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C31 |
No aliases for this group.
| derived, Hall | #22575711 ⋊ C4 |
| Sylow | C312 ⋊ Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | #22575711 | C4 |
| Frattini | C3 | #26040355 |
| Fitting, socle | C3×C312 | Dic3 |
| prime radical | C3×C31⋊D31 | D3 |
| cosocle | #31772345 | C2 |
| LCS | G ▷ #22575711 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 558 |
Polycyclic presentation:
2^2,3,31^2,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^26e^5,e^a=de^5,f^a=f^2,d^b=d^30,e^b=e^30,d^c=d^25e^7,e^c=e^5252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 69);