Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C32×C4 ⋊ SD16 |
| Sylow | C32 ⋊ #2014 |
592 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^7,3^2|a^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2i,i^a=hi,c^b=cf,d^b=dg,e^b=eg,h^b=hi,i^b=i^2,d^c=dg,e^c=eg,h^c=hi,i^c=i^2,h^d=h^2i^2,i^d=h^2i,h^e=h^2i^2,i^e=h^2i,h^g=h^2,i^g=i^242 conjugacy classes — view the full character table.
| maximal subgroup of | #72220446, #72220539, #72220547, … |
| maximal normal subgroup of | #72220446, #72220539, #72220547 |
| maximal quotient of | #72220798, #72252973 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26582);