Finite Group DatabasebetaFinite Group Databasebeta| order | 19012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C7⋊#87604 |
| unambiguous semidirect product | C7⋊(C7×#87604) |
| Fitting, socle, Hall | C72×C97 ⋊ C4 |
| derived | C7×C97 ⋊ C4×C7 |
| Sylow | C97 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ #87604 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊#87604 |
| commutator, hypocenter | C7×C97 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C97 | C4 |
| prime radical | C72×D97 | C2 |
| cosocle | C7×D97 | C2×C7 |
| LCS | G ▷ C7×C97 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1358 |
1246 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19012, 20);