Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C13×C67 ⋊ C2×C32 |
| Hall | C13⋊C3×C67⋊C3 ⋊ C2 |
| Hall | C13×D67 ⋊ C32 |
| Hall | D67 ⋊ C3×C13⋊C3 |
| Sylow | C67 ⋊ C2×C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C67 | C2×C32 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 871 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D67⋊C3, C2×C13⋊C3×D67⋊C3 |
| maximal normal subgroup of | D13⋊C3×D67⋊C3, C2×C13⋊C3×D67⋊C3 |
| maximal quotient of | C13⋊C3×(C67⋊C3)⋊C4, C2×C13⋊C3×D67⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 28);