Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C587 ⋊ C2 |
| Sylow | C587 ⋊ #123 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
Polycyclic presentation:
2^5,587|c^2=d,b^a=bd,c^a=ce,f^a=f^586,f^c=f^5862944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49177271, #123×D587, C2×#34037605, … |
| maximal normal subgroup of | #49177271, #123×D587, C2×#34037605, … |
| maximal quotient of | #49176941, #49176955, #49176957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 130);