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×#66526 ⋊ C4 |
| Hall | Dic1073 ⋊ C9 |
| Hall | #66526 ⋊ Dic29 |
| Sylow | C37 ⋊ C9×Dic29 |
| Sylow | C29 ⋊ #13050625 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C29⋊(#66526⋊C2) |
| commutator, hypocenter | C29×C37 | C4×C9 |
| Fitting, socle | C2×C29×C37 | C2×C9 |
| prime radical, cosocle | C2×C29×C37⋊C3 | C2×C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4292 |
Polycyclic presentation:
2,3^2,29,37,2|a^2=f,b^3=c,d^a=d^28,e^a=e^36,e^b=e^16,e^c=e^26404 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38628, 55);