Finite Group DatabasebetaFinite Group Databasebeta| order | 22768 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1423⋊C16 |
| derived, Sylow | C1423 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D1423 |
| commutator, hypocenter | C1423 | C16 |
| Fitting, cosocle | C8×C1423 | C2 |
| socle, prime radical | C2×C1423 | C8 |
| LCS | G ▷ C1423 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22768 |
Polycyclic presentation:
2^4,1423|a^2=b,b^2=c,c^2=d,e^a=e^14225704 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22768, 15);