Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #23751214⋊C2 |
| unambiguous semidirect product | #23751215⋊C2 |
| unambiguous semidirect product | #23751216⋊C2 |
| Fitting, socle, derived, Sylow | C312 ⋊ C22×C5 |
| Hall | #18012457 ⋊ C22 |
| Hall | D312 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C312 | C22×C5 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 310 |
Polycyclic presentation:
2^2,5,31^2|e^a=e^30,d^b=d^30,d^c=d^16,e^c=e^877 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 43);