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Cayley diagramAliases
Subgroups
38 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 12 points:
(1,2,3,4,5,6,7,8);(9,10);(11,12)
Conjugacy classes & character table
32 conjugacy classes — view the full character table.
Relationships
| center of | #1374, #1726, C8×C22⋊C4, … |
| derived subgroup of | #7076, #7077, #7078, … |
| Frattini subgroup of | #1314, #1315, #1322, … |
| Fitting subgroup of | C8×A4, A4⋊C16, #5398, … |
| maximal subgroup of | #336, #340, #341, … |
| maximal normal subgroup of | #336, #340, #341, … |
| maximal quotient of | C2×C4×C8, C2×C22⋊C8, C2×C4⋊C8, … |
| automorphism group of | C3×C32 |
| outer automorphism group of | C3×C32, #1415, #1416, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32, 36);
Finite Group Databasebeta