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Cayley diagramAliases
Subgroups
891 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 24 points:
(1,2,4,6)(3,7,8,5);(1,3,4,8)(2,5,6,7);(9,10)(11,17)(12,20)(13,15)(14,18)(16,22)(19,24)(21,23);(9,11,13,19)(10,14,15,23)(12,21,22,18)(16,24,20,17);(10,15)(14,23)(16,20)(17,24)
Conjugacy classes & character table
55 conjugacy classes — view the full character table.
Relationships
| Fitting subgroup of | SL(2,𝔽3)×#137 |
| maximal subgroup of | #250928, #250960, #250992, … |
| maximal normal subgroup of | #250928, #250960, #250992, … |
| maximal quotient of | Q8×#419, Q8×#417, C4⋊C4×#137, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(256, 54356);
Finite Group Databasebeta