Finite Group DatabasebetaFinite Group Databasebeta| order | 12051 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C13×C103 ⋊ C32 |
| Sylow | C103 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C103 | C32 |
| LCS | G ▷ C13×C103 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
259 conjugacy classes — view the full character table.
| maximal subgroup of | (C13⋊C3)⋊(D103⋊C3), D13⋊C3×C103⋊C3, C13⋊C3×D103⋊C3, … |
| maximal normal subgroup of | (C13⋊C3)⋊(D103⋊C3), D13⋊C3×C103⋊C3, C13⋊C3×D103⋊C3, … |
| maximal quotient of | C2×C13⋊C3×C103⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12051, 7);