Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C31 |
No aliases for this group.
| derived, Sylow | C312 ⋊ C4×C5 |
| Hall | #18012458 ⋊ C4 |
| Hall | C31⋊Dic31 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #23751218 |
| commutator, hypocenter | C312 | C4×C5 |
| Fitting, socle, cosocle | C2×C312 | C2×C5 |
| prime radical | C2×#18012458 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 620 |
Polycyclic presentation:
2,5,31^2,2|a^2=e,c^a=c^30,d^a=d^30,c^b=c^16,d^b=d^2212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 27);