Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #137×C283 ⋊ C2 |
| Sylow | C283 ⋊ #578 |
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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=f,e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^282,d^c=df,g^d=g^2821573 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49133031, #49133033, #49133035, … |
| maximal normal subgroup of | #49133031, #49133033, #49133035, … |
| maximal quotient of | #49129792, #49129793, #49129860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1365);