Finite Group DatabasebetaFinite Group Databasebeta| order | 19012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D679 |
| unambiguous semidirect product | (C7×D7)⋊D97 |
| unambiguous semidirect product | (D7×C97)⋊D7 |
| Fitting, socle, derived, Hall | C72×C97 ⋊ C22 |
| Sylow | C97 ⋊ D72 |
| Sylow | C72 ⋊ C2×D97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C97 | C22 |
| LCS | G ▷ C72×C97 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1358 |
1705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19012, 25);