Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C23×C3×C8 ⋊ D3 |
670 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^2,2^2|b^2=e,c^2=d,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,h^a=hi,h^f=i,i^f=hi108 conjugacy classes — view the full character table.
| maximal subgroup of | #72269839 |
| maximal quotient of | #72269839 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157000);