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Aliases
Splittings
Subgroups
48 conjugacy classes of subgroups.
Full subgroup data →
Presentation
Polycyclic presentation:
2^2,3,2^3,7|a^2=f,b^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^6,d^b=de,e^b=ef,g^c=g^4
Conjugacy classes & character table
40 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | #89687⋊C3, #89688⋊C3, Q32×AGL(1,𝔽7), … |
| maximal normal subgroup of | #89687⋊C3, #89688⋊C3, Q32×AGL(1,𝔽7), … |
| maximal quotient of | #89284⋊C3, #89287⋊C3, #89359⋊C3, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 39);
Finite Group Databasebeta