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Aliases
Splittings
Subgroups
276 conjugacy classes of subgroups.
Full subgroup data →
Presentation
Polycyclic presentation:
3,2^8|b^2=h,c^2=i,d^2=g,e^2=f,b^a=cdei,c^a=bceh,d^a=efi,e^a=defgh,f^a=fg,g^a=f,h^a=fi,i^a=ghi,c^b=cf,d^b=dg,e^b=efg,d^c=dfg,e^c=ef
Conjugacy classes & character table
28 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72240362, #72260904, #72260906, … |
| maximal subgroup of | #72240345, C2×#13829⋊C3, #72240416, … |
| maximal normal subgroup of | #72240345, C2×#13829⋊C3, #72240416, … |
| maximal quotient of | #72210009, #72235384, #72235387, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083604);
Finite Group Databasebeta