← Prev (#140) Next (#142) →
Cayley diagramAliases
Subgroups
82 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 10 points:
(1,2);(3,4)(5,8)(6,7)(9,10);(4,7)(8,10);(3,5,6,9)(4,8,7,10)
Conjugacy classes & character table
20 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #13350, #13351, #13352, … |
| Frattini subgroup of | #1391, #1392, #1395, … |
| Fitting subgroup of | C2×#41⋊C3, C2×GU(2,𝔽3), #5423, … |
| maximal subgroup of | #408, #410, #413, … |
| maximal normal subgroup of | #408, #410, #413, … |
| maximal quotient of | C2×#117, C2×C4×D4, C2×C4×Q8, … |
| automorphism group of | C2×C16, M32 |
| outer automorphism group of | C2×C16, C22⋊C16, C4⋊C16, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32, 48);
Finite Group Databasebeta