Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #10593244 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| derived | C3×C22⋊A4 ⋊ C2×C4 |
509 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 509 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3^2,2^4|a^2=c,b^2=c,e^a=e^2,f^a=fh,g^a=gi,d^b=d^2,f^b=fg,h^b=hi,f^d=g,g^d=fg,h^d=i,i^d=hi48 conjugacy classes — view the full character table.
| maximal subgroup of | #72228416, #72229182, D3×#1020⋊C4, … |
| maximal normal subgroup of | #72228416, #72229182, D3×#1020⋊C4, … |
| maximal quotient of | C2×#11920748 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154759);