Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C283 ⋊ #461 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^282,e^c=ef1993 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #461×D283, C2×#31826668, #49130712, … |
| maximal normal subgroup of | #461×D283, C2×#31826668, #49130712, … |
| maximal quotient of | #49120634, #49120638, #49120648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 752);