Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C32×#120 ⋊ C4 |
| Sylow | C32 ⋊ #1889 |
1240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=df,b^a=bd,c^a=ce,e^a=eg,h^a=h^2i^2,i^a=h^2i,e^b=eg,h^b=hi,i^b=hi^2,d^c=dg,f^c=fg,h^f=h^2,i^f=i^260 conjugacy classes — view the full character table.
| maximal subgroup of | #72241537, #72241543, #157×B(4,𝔽2), … |
| maximal normal subgroup of | #72241543, #157×B(4,𝔽2), #72242747 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 21946);