Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C283 ⋊ C2 |
| Sylow | C283 ⋊ #408 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=e,e^2=f,b^a=bd,g^a=g^282,c^b=cf,g^b=g^2822848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119198, #49121210, #49121223, … |
| maximal normal subgroup of | #49119198, #49121210, #49121223, … |
| maximal quotient of | #49119610, #49119614, #49119618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 517);