Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C32×M32 ⋊ C22 |
| Sylow | C32 ⋊ C2×#361 |
557 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 557 conjugacy classes of subgroups — too many to draw. Only its 92 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=e,d^2=f,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,i^a=hi^2,d^b=dfg,e^b=eg,f^b=fg,i^b=hi^2,h^c=h^2,i^c=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | #72222793, D32×#361, #72222843, … |
| maximal normal subgroup of | #72222793, D32×#361, #72222843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30904);