Finite Group DatabasebetaFinite Group Databasebeta| order | 15306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2551 |
| Fitting, socle, Hall | C3×C2551 ⋊ C2 |
| derived, Sylow | C2551 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2551 |
| commutator, cosocle, hypocenter | C2551 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C2551 | C2 |
| LCS | G ▷ C2551 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7653 |
3831 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D2551, C2×C3×D2551 |
| maximal normal subgroup of | D3×D2551, C2×C3×D2551 |
| maximal quotient of | C3×Dic2551, C2×C3×D2551 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15306, 4);