Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#13050607 |
| derived, Hall | C23×C37 ⋊ C4×C9 |
| Hall | C23×#66524 ⋊ C4 |
| Hall | Dic851 ⋊ C9 |
| Hall | #66524 ⋊ Dic23 |
| Sylow | C37 ⋊ C9×Dic23 |
| Sylow | C23 ⋊ #13050607 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C23⋊(D37⋊C3) |
| commutator, hypocenter | C23×C37 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C23×C37 | C2×C3 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30636 |
Polycyclic presentation:
2,3,23,37,2,3|a^2=e,b^3=f,c^a=c^22,d^a=d^36,d^b=d^261062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 12);