Finite Group DatabasebetaFinite Group Databasebeta| order | 21752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D2719 |
| Fitting | C22×C2719 ⋊ C2 |
| Sylow | C2719 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D2719 |
| commutator, socle, cosocle | C2×C2719 | C22 |
| Fitting | C22×C2719 | C2 |
| hypercenter | C22 | D2719 |
| hypocenter | C2719 | D4 |
| LCS | G ▷ C2×C2719 ▷ C2719 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10876 |
Polycyclic presentation:
2^3,2719|b^a=bc,d^b=d^27185441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21752, 9);