Finite Group DatabasebetaFinite Group Databasebeta| order | 22768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D4×D1423 |
| Fitting | D4×C1423 ⋊ C2 |
| Sylow | C1423 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1423 |
| commutator, socle, cosocle | C2×C1423 | C23 |
| Fitting | D4×C1423 | C2 |
| hypercenter | D4 | D1423 |
| hypocenter | C1423 | C2×D4 |
| LCS | G ▷ C2×C1423 ▷ C1423 | |
| UCS | C1 ◁ C2 ◁ D4 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5692 |
3565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22768, 34);