Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C22×C3×SD16 ⋊ D3 |
732 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 69 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:
2^5,3^2,2^2|c^2=e,d^2=e,c^a=ce,f^a=f^2,g^a=g^2,h^a=hi,c^b=cd,d^b=de,d^c=de,h^f=i,i^f=hi57 conjugacy classes — view the full character table.
| maximal subgroup of | #72228286, AGL(1,ℤ/8)×C3⋊S4, S4×#914, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×C3⋊S4, S4×#914, D3×#85460 |
| maximal quotient of | #72228286 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157020);