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Cayley diagramAliases
Subgroups
118 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 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 | C4×#95, C2×#336, C2×#376, … |
| derived subgroup of | #9914, #9915, #9916, … |
| Frattini subgroup of | #1280, #1282, #1284, … |
| Fitting subgroup of | C2×C4×A4, C2×A4⋊C8, #5409, … |
| socle of | #72258267, #72261521, #72263563, … |
| maximal subgroup of | C2×#95, C4×C22⋊C4, #380, … |
| maximal normal subgroup of | C2×#95, C4×C22⋊C4, #380, … |
| maximal quotient of | C22×C42, C22×C22⋊C4, C22×C4⋊C4, … |
| automorphism group of | C3×C5×C8 |
| outer automorphism group of | C3×C5×C8, D4⋊C16, #1331, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32, 45);
Finite Group Databasebeta