Finite Group DatabasebetaFinite Group Databasebeta| order | 15026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D683⋊C11 |
| unambiguous semidirect product | (C683⋊C11)⋊C2 |
| Fitting, socle, derived, Sylow | C683 ⋊ C2×C11 |
| Hall | C683⋊C11 ⋊ C2 |
| Hall | D683 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C683 | C2×C11 |
| LCS | G ▷ C683 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 683 |
Polycyclic presentation:
2,11,683|c^a=c^682,c^b=c^65153 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D683⋊C11 |
| maximal normal subgroup of | C2×D683⋊C11 |
| maximal quotient of | Dic683⋊C11, C2×D683⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15026, 1);