Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C3×C8 ⋊ C2×D3 |
618 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 51 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=d,d^2=e,c^a=cd,d^a=de,g^a=g^2,c^b=cd,d^b=de,f^b=f^2,h^b=hi,h^f=i,i^f=hi57 conjugacy classes — view the full character table.
| maximal subgroup of | #72274478, D3×SD16×S4, #72274510 |
| maximal normal subgroup of | #72274478, D3×SD16×S4, #72274510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155814);