Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C293 ⋊ C2 |
| Sylow | C293 ⋊ #543 |
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^d=g^2922066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49157706, #49157709, #49157740, … |
| maximal normal subgroup of | #49157706, #49157709, #49157740, … |
| maximal quotient of | #49161396, #49161398, #49161512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1174);