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 ⋊ #407 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4528 |
Polycyclic presentation:
2^6,283|a^2=e,e^2=f,b^a=bd,c^a=cf,g^b=g^2822848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119196, #49121180, #49121183, … |
| maximal normal subgroup of | #49119196, #49121180, #49121183, … |
| maximal quotient of | #49119587, #49119590, #49119593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 512);