Finite Group DatabasebetaFinite Group Databasebeta| order | 38628 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C29×C37 ⋊ C4×C9 |
| Hall | C29×#66526 ⋊ C4 |
| Hall | #16864282 ⋊ C9 |
| Hall | #66526 ⋊ #1181 |
| Sylow | C37 ⋊ C9×#1181 |
| Sylow | C29 ⋊ #13050625 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C37 | C4×C9 |
| prime radical, cosocle | D29×C37⋊C3 | C2×C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1073 |
Polycyclic presentation:
2,3,2,3,29,37|a^2=c,b^3=d,e^a=e^17,f^a=f^36,f^b=f^16,e^c=e^28,f^d=f^26131 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38628, 81);