Finite Group DatabasebetaFinite Group Databasebeta| order | 26894 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D113⋊C7) |
| unambiguous semidirect product | (C113⋊C7)⋊D17 |
| unambiguous semidirect product | D1921⋊C7 |
| Fitting, socle, derived, Hall | C17×C113 ⋊ C2×C7 |
| Hall | C17×C113⋊C7 ⋊ C2 |
| Hall | D1921 ⋊ C7 |
| Hall | C113⋊C7 ⋊ D17 |
| Sylow | C113 ⋊ C7×D17 |
| Sylow | C17 ⋊ D113⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C113 | C2×C7 |
| LCS | G ▷ C17×C113 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1921 |
Polycyclic presentation:
2,7,17,113|c^a=c^16,d^a=d^112,d^b=d^49206 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26894, 12);