Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22583586 |
| Fitting | C22×Q8×C283 ⋊ C2 |
| Sylow | C283 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9056 |
2848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49121565, #49121570, #49121681, … |
| maximal normal subgroup of | #49121565, #49121570, #49121681, … |
| maximal quotient of | C2×#31826322, C2×#31826336, C2×#31826346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1044);