Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C587 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
Polycyclic presentation:
2^5,587|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^5862944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D587, C2×#34037598, #49177586, … |
| maximal normal subgroup of | C22⋊Q8×D587, C2×#34037598, #49177586, … |
| maximal quotient of | #49176938, #49176952, #49176955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 123);