Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #1311 |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
Polycyclic presentation:
2^7,3^2|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=bg,h^a=h^2,i^a=i^2336 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#1311, #72245401, #72245513, … |
| maximal normal subgroup of | C3⋊D3×#1311, #72245401, #72245513, … |
| maximal quotient of | #72245300 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5308);