Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#19104951 |
| Fitting, socle | C3×C13×C67 ⋊ C2×C3 |
| derived, Hall | C13×C67 ⋊ C2×C32 |
| Hall | C3×#14579732 ⋊ C2 |
| Hall | D871 ⋊ C32 |
| Sylow | C67 ⋊ C3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19104951 |
| commutator, cosocle, hypocenter | C13×C67 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C67 | C2×C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2613 |
453 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#19104943⋊C2, D3×#19104951, #19104951⋊D3, … |
| maximal normal subgroup of | C3×#19104943⋊C2, D3×#19104951, #19104951⋊D3, … |
| maximal quotient of | C3×#23782981, C2×C3×#19104951 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 33);