Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#17989777 |
| Sylow | C293 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^2924712 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49156708, #49156709, #49156710, … |
| maximal normal subgroup of | #49156708, #49156709, #49156710, … |
| maximal quotient of | #49156709, #49156725, D4⋊#17989777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 329);