Finite Group DatabasebetaFinite Group Databasebeta| order | 22912 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#26038227 |
| Fitting | C2×#100×C179 ⋊ C2 |
| Sylow | C179 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2864 |
1984 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22912, 6143);