Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C8×C293 ⋊ C2 |
| Sylow | C293 ⋊ #465 |
124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 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=d,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^2924694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #465×D293, C2×#34036358, #49168361, … |
| maximal normal subgroup of | #465×D293, C2×#34036358, #49168361, … |
| maximal quotient of | #49158126, #49158133, #49158160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 778);