Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D31×ΓL(1,𝔽32) |
| Fitting, socle | C2×C312 ⋊ C2×C5 |
| derived, Sylow | C312 ⋊ C22×C5 |
| Hall | C31×ΓL(1,𝔽32) ⋊ C22 |
| Hall | C2×C31×D31 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D31×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C312 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C312 | C2×C5 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 620 |
374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 48);