Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×Q8×C293 ⋊ C2 |
| Sylow | C293 ⋊ #536 |
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 111 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|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^292,c^b=ce2942 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49159304, #49159320, #49159322, … |
| maximal normal subgroup of | #49159304, #49159320, #49159322, … |
| maximal quotient of | #49161371, #49161378, #49161409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1123);