Finite Group DatabasebetaFinite Group Databasebeta| order | 15994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D727⋊C11 |
| unambiguous semidirect product | (C727⋊C11)⋊C2 |
| Fitting, socle, derived, Sylow | C727 ⋊ C2×C11 |
| Hall | C727⋊C11 ⋊ C2 |
| Hall | D727 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C727 | C2×C11 |
| LCS | G ▷ C727 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 727 |
Polycyclic presentation:
2,11,727|c^a=c^726,c^b=c^66255 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D727⋊C11 |
| maximal normal subgroup of | C2×D727⋊C11 |
| maximal quotient of | Dic727⋊C11, C2×D727⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15994, 1);