Finite Group DatabasebetaFinite Group Databasebeta| order | 18486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C13×C79 ⋊ C2×C32 |
| Hall | C13⋊C3×C79⋊C3 ⋊ C2 |
| Hall | D1027 ⋊ C32 |
| Sylow | C79 ⋊ C3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C79 | C2×C32 |
| LCS | G ▷ C13×C79 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1027 |
Polycyclic presentation:
2,3^2,13,79|d^a=d^12,e^a=e^78,e^b=e^23,d^c=d^3115 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D79⋊C3, C2×(C13⋊C3)⋊(D79⋊C3) |
| maximal normal subgroup of | D13⋊C3×D79⋊C3, C2×(C13⋊C3)⋊(D79⋊C3) |
| maximal quotient of | (C79⋊C3)⋊(Dic13⋊C3), C2×(C13⋊C3)⋊(D79⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18486, 41);