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Cayley diagramAliases
Subgroups
78 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 12 points:
(3,4);(1,2)(3,4);(5,6,8,10)(7,11,12,9);(5,7,8,12)(6,9,10,11)
Conjugacy classes & character table
20 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | C22⋊SL(2,𝔽3), #393⋊C3, #395⋊C3, … |
| Frattini subgroup of | #1394, C2×#1394, #12585, … |
| Fitting subgroup of | C22×SL(2,𝔽3), Q8×A4, C22⋊SL(2,𝔽3), … |
| maximal subgroup of | #391, #393, #395, … |
| maximal normal subgroup of | #391, #393, #395, … |
| maximal quotient of | C22×C4⋊C4, C2×C4×Q8, C2×C22⋊Q8, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32, 47);
Finite Group Databasebeta