Finite Group DatabasebetaFinite Group Databasebeta| order | 21868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D77⋊D71 |
| unambiguous semidirect product | D497⋊D11 |
| unambiguous semidirect product | D781⋊D7 |
| Fitting, socle, derived, Hall | C7×C11×C71 ⋊ C22 |
| Hall | C11×C71 ⋊ C2×D7 |
| Hall | C7×C71 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×D71 |
| Sylow | C71 ⋊ D7×D11 |
| Sylow | C11 ⋊ D7×D71 |
| Sylow | C7 ⋊ D11×D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C71 | C22 |
| LCS | G ▷ C7×C11×C71 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5467 |
Polycyclic presentation:
2^2,7,11,71|d^a=d^10,e^a=e^70,c^b=c^6,d^b=d^101435 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21868, 25);