Finite Group DatabasebetaFinite Group Databasebeta| order | 988 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D19 |
| unambiguous semidirect product | C19⋊(C22×C13) |
| unambiguous semidirect product | (C2×C19)⋊(C2×C13) |
| Fitting, socle | C2×C13×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C22×C13 |
| Hall | C13×C19 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D19 |
| commutator, cosocle, hypocenter | C19 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C19 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C13 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 494 |
286 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×Dic13, #14520340, #14520341, … |
| maximal normal subgroup of | D19×Dic13, #14520340, #14520341, … |
| maximal quotient of | C13×Dic38, C4×C13×D19, C13×D76, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(988, 8);