Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3 |
No aliases for this group.
| Fitting | C32×#386 ⋊ C2 |
| Sylow | C32 ⋊ C4×#120 |
3672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=g,d^2=g,b^a=be,c^a=cf,h^a=h^2,i^a=i^2,h^c=h^2,i^c=i^2,h^d=h^2,i^d=i^2168 conjugacy classes — view the full character table.
| maximal subgroup of | #72230349, C4×C3⋊D3×#120, #72260293 |
| maximal normal subgroup of | C4×C3⋊D3×#120, #72260293 |
| maximal quotient of | #72230349 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 35998);