Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊Q8×C283 ⋊ C2 |
| Sylow | C283 ⋊ #465 |
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|b^2=d,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^282,g^b=g^2821996 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #465×D283, C2×#31826696, #49130839, … |
| maximal normal subgroup of | #465×D283, C2×#31826696, #49130839, … |
| maximal quotient of | #49120604, #49120611, #49120638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 780);