Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×C22⋊C4×D281 |
| Fitting | C2×C22⋊C4×C281 ⋊ C2 |
| Sylow | C281 ⋊ C22×C22⋊C4 |
674 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4496 |
2840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #323×D281, #49093628, #342×D281, … |
| maximal normal subgroup of | #323×D281, #49093628, #342×D281, … |
| maximal quotient of | C2×#95×D281, C4×C22⋊C4×D281, C2×#31823310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 995);