Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C67 ⋊ C2×C9 |
| Hall | #21463203 ⋊ C2 |
| Hall | D13×C67 ⋊ C9 |
| Sylow | C67 ⋊ D13⋊C9 |
| Hall | D13 ⋊ C67⋊C9 |
| Sylow | C13 ⋊ C2×C67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #19104948 |
| commutator, hypocenter | C13×C67 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C67 | C2×C3 |
| prime radical | C3×D13×C67 | C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
Polycyclic presentation:
2,3,13,67,3|b^3=e,c^a=c^12,c^b=c^3,d^b=d^29552 conjugacy classes — view the full character table.
| maximal subgroup of | #44535591, #44535593, #30627894⋊C2, … |
| maximal normal subgroup of | #44535591, #44535593, #30627894⋊C2, … |
| maximal quotient of | #44535584, C2×#30627898 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 20);