Finite Group DatabasebetaFinite Group Databasebeta| order | 18291 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×#63271 |
| Fitting, socle, Hall | C7×C13×C67 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C3×C67 |
| Hall | C13×C67 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C67 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C67 |
| Sylow | C7 ⋊ C13⋊C3×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | #63271 |
| commutator, cosocle, hypocenter | C7×C13 | C3×C67 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C67 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C67 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6097 |
2211 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C67×#63271, D67×#63271, C67×#10587717, … |
| maximal normal subgroup of | C2×C67×#63271, D67×#63271, C67×#10587717, … |
| maximal quotient of | C2×C67×#63271 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18291, 12);