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Cayley diagramC23×C42 #3418
Aliases
Subgroups
1500 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 14 points:
(1,2,3,4);(5,6,7,8);(9,10);(11,12);(13,14)
Conjugacy classes & character table
128 conjugacy classes — view the full character table.
Relationships
| center of | C42×#95, C22×#1273, C2×C4×#336, … |
| derived subgroup of | #72228201, #72239000, #72239012, … |
| Frattini subgroup of | #92807, #92808, #92812, … |
| Fitting subgroup of | C23×C42⋊C3, C2×C42×A4, C2×C22⋊(C42⋊C3), … |
| socle of | C22×C4×#525, C2×C4×#2388, C22×#34547, … |
| maximal subgroup of | #7554, #10712, #10719, … |
| maximal normal subgroup of | #7554, #10712, #10719, … |
| maximal quotient of | C22×C43, C23×#95, C22×#376, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2150);
Finite Group Databasebeta