Finite Group DatabasebetaFinite Group Databasebeta| order | 38628 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C29×C37 ⋊ C4×C9 |
| Hall | C29×#66524 ⋊ C4 |
| Hall | #16864281 ⋊ C9 |
| Hall | #66524 ⋊ #1181 |
| Sylow | C37 ⋊ C9×#1181 |
| Sylow | C29 ⋊ #13050613 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16864281⋊C3 |
| commutator, hypocenter | C29×C37 | C4×C9 |
| Fitting, socle | C3×C29×C37 | C3×C4 |
| prime radical, cosocle | C3×D1073 | C2×C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9657 |
Polycyclic presentation:
2,3,2,29,37,3|a^2=c,b^3=f,d^a=d^17,e^a=e^6,e^b=e^26,d^c=d^28,e^c=e^36360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38628, 16);