Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C32×#120 ⋊ C22 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
2367 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 2367 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^7,3^2|b^a=be,c^a=cf,f^b=fg,e^c=eg,i^c=hi^2,h^d=h^2,i^d=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72210357, #72214743, #72214786, … |
| maximal normal subgroup of | #72214743, #72214786, C3×#11865254, … |
| maximal quotient of | #72220167, C3×#11865254, #72220851, … |
| holomorph of | C2×Dic3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99265);