Finite Group DatabasebetaFinite Group Databasebeta| order | 12353 |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1123⋊C11 |
| Fitting, socle, derived, Sylow | C1123 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1123 | C11 |
| LCS | G ▷ C1123 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
11,1123|b^a=b^848113 conjugacy classes — view the full character table.
| maximal subgroup of | D1123⋊C11, C2×C1123⋊C11, (C1123⋊C3)⋊C11, … |
| maximal normal subgroup of | D1123⋊C11, C2×C1123⋊C11, (C1123⋊C3)⋊C11, … |
| maximal quotient of | C2×C1123⋊C11, C3×C1123⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12353, 1);