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Cayley diagramAliases
Subgroups
748 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 13 points:
(1,2)(11,12,13);(3,4);(5,6);(7,8);(9,10)
Conjugacy classes & character table
96 conjugacy classes — view the full character table.
Relationships
| center of | C22×C3×#95, C23×C3×C22⋊C4, C23×C3×C4⋊C4, … |
| derived subgroup of | #10698138, #10698139, #10698140, … |
| Frattini subgroup of | C9×#1304, C9⋊#1304, #1304⋊C9, … |
| Fitting subgroup of | #5247, C22×#217, C2×#953, … |
| socle of | C24×Dic3, C24×C3×C4, C25×D3, … |
| maximal subgroup of | #5247, C3×#379, C22×#217, … |
| maximal normal subgroup of | #5247, C3×#379, C22×#217, … |
| maximal quotient of | C24×C3×C4, C23×C3×D4, C23×C3×Q8, … |
| outer automorphism group of | #6487, C4×C22⋊D7, #6493, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 231);
Finite Group Databasebeta