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×D4 ⋊ D3 |
848 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 848 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) = 72 |
Polycyclic presentation:
2^5,3^2,2^2|b^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,h^a=hi,c^b=ce,d^c=de,h^f=i,i^f=hi72 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×C3⋊S4, #72258944, D3×#85489, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×C3⋊S4, D3×#85489, S4×#932 |
| maximal quotient of | #72258944 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157049);