Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C293 ⋊ C2 |
| Sylow | C293 ⋊ #576 |
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 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|e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^292,d^c=df2504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49170546, #49170547, #49170549, … |
| maximal normal subgroup of | #49170546, #49170547, #49170549, … |
| maximal quotient of | #49167308, #49167311, #49167383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1352);