Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #10588305 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C22⋊(C22⋊C9) ⋊ C8 |
148 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^2,2^4|a^2=b,b^2=c,d^3=e,d^a=d^2e^2,e^a=e^2,f^a=fgh,g^a=ghi,h^a=hi,f^b=fh,g^b=gi,f^d=g,g^d=fg,h^d=i,i^d=hi42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153937);