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Cayley diagramAliases
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,3,4)(7,8,9,10,11,12,13);(5,6)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| center of | C7×#97, C7×C22⋊C8, C7×C4⋊C8, … |
| derived subgroup of | #89246, #89247, #89259, … |
| Frattini subgroup of | C4×C49⋊C8, #13095843, C4⋊(C49⋊C8), … |
| Fitting subgroup of | C2×C7⋊C8, #1136, C4×Dic7, … |
| maximal subgroup of | C2×C7⋊C8, #1136, C4×Dic7, … |
| maximal normal subgroup of | C2×C7⋊C8, #1136, C4×Dic7, … |
| maximal quotient of | C42×C7, C7×C22⋊C4, C7×C4⋊C4, … |
| automorphism group of | C3×C29, C4×C29, C2×C3×C29 |
| outer automorphism group of | C3×C29, C4×C29, C2×C3×C29, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(56, 8);
Finite Group Databasebeta