Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C283 ⋊ #455 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4528 |
Polycyclic presentation:
2^6,283|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^282,d^b=df,e^b=ef,d^c=df2413 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49123248, #49123249, #49123260, … |
| maximal normal subgroup of | #49123248, #49123249, #49123260, … |
| maximal quotient of | #49120213, #49120218, #49120241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 727);