Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #106×C283 ⋊ C2 |
| Sylow | C283 ⋊ #428 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^c=g^2821996 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #428×D283, C2×#31826504, #49129848, … |
| maximal normal subgroup of | #428×D283, C2×#31826504, #49129848, … |
| maximal quotient of | #49120010, #49120025, #49120043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 588);