Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C283 ⋊ C2 |
| Sylow | C283 ⋊ #519 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,g^d=g^2822854 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49130097, #49130099, #49130101, … |
| maximal normal subgroup of | #49130097, #49130099, #49130101, … |
| maximal quotient of | #49123615, #49123625, #49123626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1025);