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Cayley diagramAliases
Subgroups
66 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 10 points:
(1,2);(4,6)(7,8,9,10);(3,4)(5,6)(7,8)(9,10)
Conjugacy classes & character table
20 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #7394, #7395, #7426, … |
| Frattini subgroup of | #1316, #1317, #1326, … |
| Fitting subgroup of | C2×C22⋊C4×A5, C22⋊C4×SL(2,𝔽5), C2×#11751534, … |
| maximal subgroup of | #323, #342, C4×C22⋊C4, … |
| maximal normal subgroup of | #323, #342, C4×C22⋊C4, … |
| maximal quotient of | C2×#95, C4×C22⋊C4, #379, … |
| outer automorphism group of | #125, #433, #4543, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32, 22);
Finite Group Databasebeta