Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #1368 |
204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,d^b=dg,h^b=h^2,i^b=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#1368, #72222562, #72222571, … |
| maximal normal subgroup of | C3⋊D3×#1368, #72222562, #72222571, … |
| maximal quotient of | #72245513, #72245532, #72245542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6187);