Finite Group DatabasebetaFinite Group Databasebeta| order | 26996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D397 |
| unambiguous semidirect product | (D17×C397)⋊C2 |
| unambiguous semidirect product | (C17×D397)⋊C2 |
| unambiguous semidirect product | D6749⋊C2 |
| Fitting, socle, derived, Hall | C17×C397 ⋊ C22 |
| Sylow | C397 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C397 | C22 |
| LCS | G ▷ C17×C397 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6749 |
2000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26996, 12);