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Cayley diagramAliases
Subgroups
133 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 18 points:
(1,2);(3,4,6,9,7,10,13,16)(5,8,12,15,11,14,17,18);(3,5)(4,8)(6,12)(7,11)(9,15)(10,14)(13,17)(16,18);(5,11)(8,14)(12,17)(15,18)
Conjugacy classes & character table
40 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #142616, #142617, #142618, … |
| Frattini subgroup of | #7207, #7208, #7227, … |
| Fitting subgroup of | C2×#131⋊C3, C2×#4628, #73119, … |
| maximal subgroup of | #1757, #1764, #1765, … |
| maximal normal subgroup of | #1757, #1764, #1765, … |
| maximal quotient of | C2×#405, C4×#131, C2×#408, … |
| automorphism group of | C2×C32, M64 |
| outer automorphism group of | C2×C32, C22⋊C32, C4⋊C32, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 248);
Finite Group Databasebeta