Finite Group DatabasebetaFinite Group Databasebeta| order | 17251 |
| automorphism | ? |
| homology | Abelianization (H1) = C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1327⋊C13 |
| Fitting, socle, derived, Sylow | C1327 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1327 | C13 |
| LCS | G ▷ C1327 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
13,1327|b^a=b^1215115 conjugacy classes — view the full character table.
| maximal subgroup of | D1327⋊C13, C2×C1327⋊C13 |
| maximal normal subgroup of | D1327⋊C13, C2×C1327⋊C13 |
| maximal quotient of | C2×C1327⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17251, 1);