Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C283 ⋊ #544 |
206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 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=e,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^2821996 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49120199, #49120202, #49120233, … |
| maximal normal subgroup of | #49120199, #49120202, #49120233, … |
| maximal quotient of | #49123878, #49123880, #49123991, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1178);