Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C32×C4 ⋊ D4 |
| Sylow | C32 ⋊ #2388 |
1602 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 135 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|d^2=e,b^a=be,c^a=cf,c^b=cg,i^b=hi^2,h^c=hi,i^c=i^2,h^g=h^2,i^g=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42263);