Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C293 ⋊ #435 |
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^138,g^c=g^138,g^e=g^292758 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#34037158, D293⋊#435, #49175500, … |
| maximal normal subgroup of | C2×#34037158, D293⋊#435, #49175500, … |
| maximal quotient of | #49174384, #49174388, #49174392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1578);