← Prev (#242) Next (#244) →
Cayley diagramAliases
Subgroups
54 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 9 points:
(1,2)(3,4,5);(1,2)(7,9);(1,2)(6,7)(8,9)
Conjugacy classes & character table
30 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #67461, #67462, #67538, … |
| Frattini subgroup of | #10588148, #10588149, #10588150, … |
| Fitting subgroup of | #832, #833, #834, … |
| maximal subgroup of | #832, #833, #834, … |
| maximal normal subgroup of | #832, #833, #834, … |
| maximal quotient of | C2×C3×C22⋊C4, C2×C3×C4⋊C4, C3×C4×D4, … |
| automorphism group of | C2×C4×C7, C7×D4, C2×C4×C9, … |
| outer automorphism group of | C2×C4×C7, C2×C4×C9, C2×Dic13, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(48, 45);
Finite Group Databasebeta