Finite Group DatabasebetaFinite Group Databasebeta| order | 21868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic497 |
| unambiguous semidirect product | C7⋊(C11×Dic71) |
| unambiguous semidirect product | C71⋊(C11×Dic7) |
| derived, Hall | C7×C71 ⋊ C4×C11 |
| Hall | C7×C11×C71 ⋊ C4 |
| Hall | C11×C71 ⋊ Dic7 |
| Hall | C7×C11 ⋊ Dic71 |
| Sylow | C71 ⋊ C11×Dic7 |
| Sylow | C7 ⋊ C11×Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D497 |
| commutator, hypocenter | C7×C71 | C4×C11 |
| Frattini | C2 | C11×D497 |
| Fitting, socle, prime radical | C2×C7×C11×C71 | C2 |
| cosocle | C2×C7×C71 | C2×C11 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21868 |
5500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21868, 7);