Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #22575711 ⋊ C4 |
| Sylow | C312 ⋊ Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #31772350 |
| commutator, hypocenter | #22575711 | C4 |
| Frattini | C2×C3 | #19153449 |
| Fitting, socle, prime radical | C2×C3×C312 | D3 |
| cosocle | C2×#22575711 | C2 |
| LCS | G ▷ #22575711 | |
| UCS | C1 ◁ C2 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1116 |
Polycyclic presentation:
2,3,31^2,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=d,d^a=c,f^a=f^2,c^b=c^5,d^b=d^251062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 55);