Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #1415 |
246 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,i^a=i^2,c^b=ce,e^b=ef,f^b=fg126 conjugacy classes — view the full character table.
| maximal subgroup of | #72254948, C3⋊D3×#1415, #72269638 |
| maximal normal subgroup of | #72254948, C3⋊D3×#1415, #72269638 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6922);