Finite Group DatabasebetaFinite Group Databasebeta| order | 988 |
| isoclinism | isoclinic class of D13×D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D19 |
| unambiguous semidirect product | (C19×D13)⋊C2 |
| unambiguous semidirect product | (C13×D19)⋊C2 |
| unambiguous semidirect product | D247⋊C2 |
| Fitting, socle, derived, Hall | C13×C19 ⋊ C22 |
| Sylow | C19 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C19 | C22 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 247 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#261, C2×D13×D19, #13093360⋊C2, … |
| maximal normal subgroup of | D19×#261, C2×D13×D19, #13093360⋊C2, … |
| maximal quotient of | D19×Dic13, D13×Dic19, #14520339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(988, 7);