Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C283 ⋊ C2 |
| Sylow | C283 ⋊ #578 |
248 conjugacy classes of subgroups.
| 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,g^a=g^282,e^b=ef,g^b=g^282,d^c=df2842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49123223, #49123227, #49123237, … |
| maximal normal subgroup of | #49123223, #49123227, #49123237, … |
| maximal quotient of | #49129795, #49129861, #49130106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1366);