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Cayley diagramAliases
Subgroups
14 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);(17,18)
Conjugacy classes & character table
32 conjugacy classes — view the full character table.
Relationships
| center of | #1397, C22⋊C32, C4⋊C32, … |
| derived subgroup of | #7418, #7419, #7420, … |
| Frattini subgroup of | C4×C32, #1397, #1398, … |
| Fitting subgroup of | C2×C16×A5, C16×SL(2,𝔽5), C2×#11746446 |
| maximal subgroup of | C4×C16, #346, C22⋊C16, … |
| maximal normal subgroup of | C4×C16, #346, C22⋊C16, … |
| maximal quotient of | C4×C16, C22⋊C16, C4⋊C16, … |
| automorphism group of | C3×C17, C64, C4×C17, … |
| outer automorphism group of | C3×C17, C64, C4×C17, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32, 16);
Finite Group Databasebeta