Finite Group DatabasebetaFinite Group Databasebeta| order | 14274 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C13×C61 ⋊ C2×C32 |
| Hall | C13⋊C3×C61⋊C3 ⋊ C2 |
| Hall | D793 ⋊ C32 |
| Sylow | C61 ⋊ C3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C61 | C2×C32 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 793 |
Polycyclic presentation:
2,3^2,13,61|d^a=d^12,e^a=e^60,e^b=e^13,d^c=d^394 conjugacy classes — view the full character table.
| maximal subgroup of | #23748919⋊C3, #23748921⋊C3, D13⋊C3×D61⋊C3, … |
| maximal normal subgroup of | #23748919⋊C3, #23748921⋊C3, D13⋊C3×D61⋊C3, … |
| maximal quotient of | #23748912⋊C3, C2×(C13⋊C3)⋊(D61⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14274, 26);