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Cayley diagramAliases
Subgroups
10 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2)(5,6,7,8,9,10,11,12,13,14,15);(3,4)
Conjugacy classes & character table
44 conjugacy classes — view the full character table.
Relationships
| center of | C11×C22⋊C4, C11×C4⋊C4, C2×D4×C11, … |
| derived subgroup of | A4×D11, #66870, #66887, … |
| Frattini subgroup of | C4×Dic121, Dic121⋊C4, C4⋊Dic121, … |
| Fitting subgroup of | C2×Dic11, C22⋊D11, C22×D11, … |
| socle of | C2×Dic11, C2×C4×C11, C22×D11, … |
| maximal subgroup of | C2×Dic11, C22⋊D11, C2×C4×C11, … |
| maximal normal subgroup of | C2×Dic11, C22⋊D11, C2×C4×C11, … |
| maximal quotient of | C2×C4×C11, D4×C11, Q8×C11, … |
| automorphism group of | C3×C23, C4×C23, C2×C3×C23 |
| outer automorphism group of | C3×C23, C4×C23, C2×C3×C23, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(44, 4);
Finite Group Databasebeta