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Aliases
Splittings
Subgroups
1896 conjugacy classes of subgroups.
Full subgroup data →
Presentation
Polycyclic presentation:
3,2^8|b^2=h,c^2=h,b^a=bceg,c^a=bdeg,d^a=egh,e^a=defhi,f^a=g,g^a=fg,h^a=i,i^a=hi,c^b=ch,d^b=di,e^b=eh,d^c=dhi,e^c=ei
Conjugacy classes & character table
28 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72234218, #72234220, #72234660, … |
| maximal subgroup of | #72209702, #72209713, C2×C22⋊#5464, … |
| maximal normal subgroup of | #72209713, C2×C22⋊#5464, #72218927, … |
| maximal quotient of | #72209702, #72209711, #72210038, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085030);
Finite Group Databasebeta