Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C587 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
Polycyclic presentation:
2^5,587|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^b=f^5862941 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49177258, #49177259, #49177263, … |
| maximal normal subgroup of | #49177258, #49177259, #49177263, … |
| maximal quotient of | #49177081, #49177088, #49177123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 176);