Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D247 |
| Fitting | C22×C13×C19 ⋊ C2 |
| Hall | C13×C19 ⋊ D4 |
| Sylow | C19 ⋊ C22⋊D13 |
| Sylow | C13 ⋊ C22⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D247 |
| commutator, socle, cosocle | C2×C13×C19 | C22 |
| Fitting | C22×C13×C19 | C2 |
| hypercenter | C22 | D247 |
| hypocenter | C13×C19 | D4 |
| LCS | G ▷ C2×C13×C19 ▷ C13×C19 | |
| UCS | C1 ◁ C2 ◁ C22 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 988 |
Polycyclic presentation:
2^3,13,19|b^a=bc,d^a=d^12,e^a=e^18497 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 28);