← Prev (#138) Next (#140) →
Cayley diagramAliases
Subgroups
118 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 8 points:
(3,4);(1,2)(3,4);(6,8);(5,6)(7,8)
Conjugacy classes & character table
20 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #13343, #13344, #13345, … |
| Frattini subgroup of | #1390, #1393, C2×#1390, … |
| Fitting subgroup of | D4×A4, #5414, #5415, … |
| maximal subgroup of | #386, #390, #392, … |
| maximal normal subgroup of | #386, #390, #392, … |
| maximal quotient of | C22×C22⋊C4, C22×C4⋊C4, C2×C4×D4, … |
| automorphism group of | #104, C2×C3×C8, C3×M16, … |
| outer automorphism group of | C4×D4, #124, C2×M16, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32, 46);
Finite Group Databasebeta