Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C32×H(5,𝔽2) ⋊ C22 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
2485 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 2485 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|b^a=be,c^a=cf,i^a=hi^2,f^b=fg,e^c=eg,h^d=h^2,i^d=i^281 conjugacy classes — view the full character table.
| maximal subgroup of | D32×B(4,𝔽2), #72242873, #72252344, … |
| maximal normal subgroup of | D32×B(4,𝔽2), #72242873, #72252344, … |
| maximal quotient of | #72253276, #72258283 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99269);