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Aliases
Subgroups
4543 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 22 points:
(3,4)(5,6);(3,5,6,4);(4,5)(7,8,9,13,10,15,18,22,11,16,17,14,19,12,20,21);(1,2);(8,12,16,15)(9,17)(13,22,14,21)(18,20)
Conjugacy classes & character table
220 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | C2×D4×AGL(1,ℤ/16), D4×#33468, #72309663, … |
| maximal normal subgroup of | C2×D4×AGL(1,ℤ/16), D4×#33468, #72309663, … |
| maximal quotient of | C2×D4×#1313, C2×#72239256, D4×#12605, … |
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((3,4)(5,6), (3,5,6,4), (4,5)(7,8,9,13,10,15,18,22,11,16,17,14,19,12,20,21), (1,2), (8,12,16,15)(9,17)(13,22,14,21)(18,20));
Finite Group Databasebeta