← Prev (#3477) Next (#3479) →
Cayley diagramAliases
Subgroups
534 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 16 points:
(1,2,4,6)(3,7,8,5);(1,3,4,8)(2,5,6,7);(9,10)(11,14)(12,13)(15,16);(10,13)(14,16);(9,11,12,15)(10,14,13,16)
Conjugacy classes & character table
50 conjugacy classes — view the full character table.
Relationships
| Fitting subgroup of | #41×SL(2,𝔽3), Q8×#41⋊C3, #41⋊SL(2,𝔽3), … |
| maximal subgroup of | #8439, #17509, #17514, … |
| maximal normal subgroup of | #8439, #17509, #17514, … |
| maximal quotient of | C4⋊C4×#41, Q8×#117, #34145, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2210);
Finite Group Databasebeta