Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#13050625 |
| derived, Hall | C23×C37 ⋊ C4×C9 |
| Hall | C23×#66526 ⋊ C4 |
| Hall | Dic851 ⋊ C9 |
| Hall | #66526 ⋊ Dic23 |
| Sylow | C37 ⋊ C9×Dic23 |
| Sylow | C23 ⋊ #13050625 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C23⋊(#66526⋊C2) |
| commutator, hypocenter | C23×C37 | C4×C9 |
| Fitting, socle | C2×C23×C37 | C2×C9 |
| prime radical, cosocle | C2×C23×C37⋊C3 | C2×C3 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3404 |
Polycyclic presentation:
2,3^2,23,37,2|a^2=f,b^3=c,d^a=d^22,e^a=e^36,e^b=e^16,e^c=e^26326 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 43);