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Cayley diagramAliases
Subgroups
296 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 22 points:
(1,2);(7,8,10,13,11,14,17,20)(9,12,16,19,15,18,21,22);(3,4,5,6)(7,9)(8,12)(10,16)(11,15)(13,19)(14,18)(17,21)(20,22);(9,15)(12,18)(16,21)(19,22)
Conjugacy classes & character table
80 conjugacy classes — view the full character table.
Relationships
| Frattini subgroup of | #93286, #93287, #93325, … |
| maximal subgroup of | #8156, #8157, #8601, … |
| maximal normal subgroup of | #8156, #8157, #8601, … |
| maximal quotient of | C2×C8×M16, C2×#1450, C2×#1451, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 1604);
Finite Group Databasebeta