Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D5696 |
| Fitting | C2×C64×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×D64 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D2848 |
| commutator, cosocle | C32×C89 | C23 |
| Frattini | C32 | C22×D89 |
| Fitting | C2×C64×C89 | C2 |
| socle | C22×C89 | D32 |
| hypercenter | C2×C64 | D89 |
| hypocenter | C89 | C2×D64 |
| LCS | G ▷ C32×C89 ▷ C16×C89 ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×C64 | |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
5702 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 90611);