Finite Group DatabasebetaFinite Group Databasebeta| order | 20876 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic307⋊C17 |
| unambiguous semidirect product | (C307⋊C17)⋊C4 |
| derived, Sylow | C307 ⋊ C4×C17 |
| Hall | C307⋊C17 ⋊ C4 |
| Hall | Dic307 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D307⋊C17 |
| commutator, hypocenter | C307 | C4×C17 |
| Fitting, socle, cosocle | C2×C307 | C2×C17 |
| prime radical | C2×C307⋊C17 | C2 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1228 |
Polycyclic presentation:
2,17,307,2|a^2=d,c^a=c^306,c^b=c^8186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20876, 2);