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Cayley diagramC25 #144
Aliases
Subgroups
374 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 10 points:
(1,2);(3,4);(5,6);(7,8);(9,10)
Conjugacy classes & character table
32 conjugacy classes — view the full character table.
Relationships
| center of | C22×#95, C23×C22⋊C4, C23×C4⋊C4, … |
| derived subgroup of | #10336, #10337, #10338, … |
| Frattini subgroup of | #1304, #7554, #7555, … |
| Fitting subgroup of | C23×A4, C2×C22⋊A4, C2×C24⋊C5, … |
| socle of | C24×C4, C23×A4, C2×C22⋊A4, … |
| maximal subgroup of | #379, C22×C22⋊C4, C2×#120, … |
| maximal normal subgroup of | #379, C22×C22⋊C4, C2×#120, … |
| maximal quotient of | C24×C4, C23×D4, C23×Q8, … |
| outer automorphism group of | #436, C4×SD16, #446, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32, 51);
Finite Group Databasebeta