Finite Group DatabasebetaFinite Group Databasebeta| order | 18778 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C229 · Schur multiplier (H2) = C1 |
| direct product | D41×C229 |
| unambiguous semidirect product | C41⋊(C2×C229) |
| Fitting, socle, Hall | C41×C229 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C229 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C229 | D41 |
| commutator, cosocle, hypocenter | C41 | C2×C229 |
| Frattini | C1 | G |
| Fitting, socle | C41×C229 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C229 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9389 |
5038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #4223×C229, #49176495, D41×D229, … |
| maximal normal subgroup of | #4223×C229, #49176495, D41×D229, … |
| maximal quotient of | Dic41×C229, C2×D41×C229 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18778, 1);