Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
No aliases for this group.
| Fitting | C2×C32×D4 ⋊ Q8 |
| Sylow | C32 ⋊ #2409 |
958 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 143 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=e,b^2=e,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=hi,i^a=hi^2,c^b=cg,h^b=i,i^b=h^2,h^d=i^2,i^d=h,h^e=h^2,i^e=i^248 conjugacy classes — view the full character table.
| maximal subgroup of | #120×PSU(3,𝔽2), #72220539, #72220545, … |
| maximal normal subgroup of | #120×PSU(3,𝔽2), #72220539, #72220545, … |
| maximal quotient of | #72227605, #72227608, #72242747 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 43481);