Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×#127 ⋊ C2 |
| Sylow | C32 ⋊ #3151 |
1968 conjugacy classes of subgroups; only the 337 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 337 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,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×#3151, #72214182, #72214505, … |
| maximal normal subgroup of | C3⋊D3×#3151, #72214182, #72214505, … |
| maximal quotient of | #72214182 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 108475);