Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C32×C4 ⋊ D4 |
| Sylow | C32 ⋊ #2392 |
1122 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 127 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|a^2=f,d^2=e,b^a=be,c^a=cf,h^a=hi,i^a=hi^2,c^b=cg,i^c=hi^2,h^f=h^2,i^f=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42477);