Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C42 |
| direct product | #2840×D89 |
| Fitting | C89×#2840 ⋊ C2 |
| Sylow | C89 ⋊ C2×#2840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D89 |
| commutator, socle, cosocle | C23×C89 | C25 |
| Fitting | C89×#2840 | C2 |
| prime radical | C25×D89 | C22 |
| hypercenter | #2840 | D89 |
| hypocenter | C89 | C2×#2840 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
3550 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2848 |
1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 375974);