Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C32×Q8 ⋊ D4 |
| Sylow | C32 ⋊ #3013 |
1238 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,i^a=hi^2,e^b=eg,h^b=hi,i^b=i^2,d^c=dg,h^c=hi,i^c=i^2,h^e=h^2,i^e=i^2,h^f=h^2,i^f=i^260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98764);