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Cayley diagramAliases
Subgroups
342 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 16 points:
(1,2,3,4);(5,6,7,8);(9,10,11,12)(13,16,15,14);(9,13,11,15)(10,14,12,16)
Conjugacy classes & character table
80 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #73284, C2×#73284, #11709745, … |
| Fitting subgroup of | Q8×C42⋊C3, C42×SL(2,𝔽3), #73284, … |
| maximal subgroup of | C4×Q8⋊C8, #8171, #8173, … |
| maximal normal subgroup of | C4×Q8⋊C8, #8171, #8173, … |
| maximal quotient of | C42×C4⋊C4, C4×#387, C4×#389, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 1004);
Finite Group Databasebeta