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Cayley diagramAliases
Splittings
Subgroups
72 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 16 points:
(2,3,7)(6,9,13)(8,11,10)(14,16,15);(1,7,5,10)(2,11,8,3)(4,13,12,15)(6,16,14,9);(2,6)(3,9)(8,14)(11,16)
Polycyclic presentation:
3,2^6|d^2=g,e^2=g,b^a=c,c^a=bc,d^a=e,e^a=de,e^b=ef,d^c=df,e^d=eg
Conjugacy classes & character table
18 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #85548, #85549, #85550, … |
| maximal subgroup of | #2029⋊C3, #2030⋊C3, #2032⋊C3, … |
| maximal normal subgroup of | #2029⋊C3, #2030⋊C3, #2032⋊C3, … |
| maximal quotient of | #73291, #73293, C2×#543⋊C3, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 1021);
Finite Group Databasebeta