Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×#127 ⋊ C22 |
| Sylow | C32 ⋊ C2×#453 |
1937 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 1937 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|e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,f^b=fg,i^b=hi^2,e^c=eg,h^d=h^2,i^d=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11864777, #72214117, #72214248, … |
| maximal normal subgroup of | C2×#11864777, #72214117, #72214248, … |
| maximal quotient of | C2×#11864777, #72214414, #72219772, … |
| holomorph of | Dic6, D12 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98788);