Finite Group DatabasebetaFinite Group Databasebeta| order | 18844 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14582089⋊C7 |
| Fitting, socle, derived, Sylow | C673 ⋊ C4×C7 |
| Hall | C673⋊C7 ⋊ C4 |
| Hall | #14582089 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C673 | C4×C7 |
| prime radical | D673⋊C7 | C2 |
| cosocle | D673 | C2×C7 |
| LCS | G ▷ C673 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 673 |
Polycyclic presentation:
2,7,2,673|a^2=c,d^a=d^58,d^b=d^620,d^c=d^67252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18844, 8);