Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#21463204 |
| derived, Hall | C13×C67 ⋊ C2×C9 |
| Hall | C2×C13×C67 ⋊ C9 |
| Hall | C2×C67 ⋊ C13⋊C9 |
| Sylow | C67 ⋊ C2×C13⋊C9 |
| Hall | C2×C13 ⋊ C67⋊C9 |
| Sylow | C13 ⋊ C2×C67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #14579732 |
| commutator, hypocenter | C13×C67 | C2×C9 |
| Frattini | C3 | C2×#14579732 |
| Fitting, socle, prime radical | C2×C3×C13×C67 | C3 |
| cosocle | C3×C13×C67 | C2×C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15678 |
1758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#21463204, #44535579, #44535583, … |
| maximal normal subgroup of | C4×#21463204, #44535579, #44535583, … |
| maximal quotient of | C4×#21463204, C22×#21463204 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 4);