Finite Group DatabasebetaFinite Group Databasebeta| order | 18486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C79 ⋊ C2×C3×C13 |
| derived, Sylow | C79 ⋊ C2×C32×C13 |
| Hall | C3×(C79⋊C3)⋊C13 ⋊ C2 |
| Hall | D79⋊C13 ⋊ C32 |
| Hall | C3×D79⋊C3 ⋊ C13 |
| Hall | C79⋊C13 ⋊ C2×C32 |
| Hall | C3×C79⋊C3 ⋊ C2×C13 |
| Hall | D79 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽79) |
| commutator, cosocle, hypocenter | C79 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C79 | C2×C3×C13 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 237 |
237 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽79), C2×C3×AGL(1,𝔽79) |
| maximal normal subgroup of | D3×AGL(1,𝔽79), C2×C3×AGL(1,𝔽79) |
| maximal quotient of | C3×((C79⋊C3)⋊C4)⋊C13, C2×C3×AGL(1,𝔽79) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18486, 32);