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Cayley diagramAliases
Subgroups
1095 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 24 points:
(1,2,3,5,4,6,7,8);(9,10)(11,17)(12,15)(13,16)(14,19)(18,23)(20,22)(21,24);(9,11,13,19)(10,14,16,17)(12,20,21,18)(15,23,24,22);(9,12,13,21)(10,15,16,24)(11,18,19,20)(14,22,17,23);(10,16)(14,17)(15,24)(22,23)
Conjugacy classes & character table
136 conjugacy classes — view the full character table.
Relationships
| Fitting subgroup of | C8×2−1+4⋊C3, C8×2−1+4⋊C5 |
| maximal subgroup of | #129665, C8×#454, C8×#456, … |
| maximal normal subgroup of | #129665, C8×#454, C8×#456, … |
| maximal quotient of | C8×#520, C8×#519, C8×#536, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 53317);
Finite Group Databasebeta