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Aliases
Splittings
Subgroups
79 conjugacy classes of subgroups.
Full subgroup data →
Presentation
Polycyclic presentation:
3^2,2^6|e^a=ef,f^a=e,g^a=gh,h^a=g,c^b=cd,d^b=c,g^b=h,h^b=gh,e^c=eh,f^c=fgh,e^d=eg,f^d=fh
Conjugacy classes & character table
19 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #11921467, C2×#11921467, C3×#11921467, … |
| maximal subgroup of | #85558⋊C3, #85560⋊C3, #11921467, … |
| maximal normal subgroup of | #85558⋊C3, #85560⋊C3, #11921467, … |
| maximal quotient of | #73203⋊C3, #73210⋊C3, C2×#5450⋊C3, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5129);
Finite Group Databasebeta