Finite Group DatabasebetaFinite Group Databasebeta| order | 18894 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C47 · Schur multiplier (H2) = C1 |
| direct product | C3×C47×D67 |
| Fitting, socle, Hall | C3×C47×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C3×C47 |
| Hall | C47×C67 ⋊ C2×C3 |
| Hall | C3×C67 ⋊ C2×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C47 | D67 |
| commutator, cosocle, hypocenter | C67 | C2×C3×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C47×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C47 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9447 |
4935 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D47×D67, D3×C47×D67, D67×D141, … |
| maximal normal subgroup of | C3×D47×D67, D3×C47×D67, D67×D141, … |
| maximal quotient of | C3×C47×Dic67, C2×C3×C47×D67 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18894, 3);