Finite Group DatabasebetaFinite Group Databasebeta| order | 26978 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D287 |
| unambiguous semidirect product | C7⋊(C47×D41) |
| unambiguous semidirect product | C41⋊(D7×C47) |
| Fitting, socle, Hall | C7×C41×C47 ⋊ C2 |
| derived, Hall | C7×C41 ⋊ C2×C47 |
| Hall | C41×C47 ⋊ D7 |
| Hall | C7×C47 ⋊ D41 |
| Sylow | C41 ⋊ D7×C47 |
| Sylow | C7 ⋊ C47×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D287 |
| commutator, cosocle, hypocenter | C7×C41 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C7×C41×C47 | C2 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13489 |
6815 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26978, 7);