Finite Group DatabasebetaFinite Group Databasebeta| order | 18620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C7 |
| direct product | C19×#11758266 |
| Fitting, socle, Hall | C5×C72×C19 ⋊ C4 |
| derived, Hall | C5×C72 ⋊ C4×C19 |
| Hall | C72×C19 ⋊ AGL(1,𝔽5) |
| Hall | C5×C19 ⋊ #5997 |
| Sylow | C72 ⋊ C19×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C19×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #11758266 |
| commutator, hypocenter | C5×C72 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C19 | C4 |
| prime radical | C19×C5⋊(C7⋊D7) | C2 |
| cosocle | C5⋊(C7⋊D7) | C2×C19 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C19 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1330 |
1235 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18620, 54);