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Cayley diagramC53 #1251
Aliases
Subgroups
64 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3,4,5);(6,7,8,9,10);(11,12,13,14,15)
Conjugacy classes & character table
125 conjugacy classes — view the full character table.
Relationships
| center of | C53×D3, C53×D5, C53×A4, … |
| derived subgroup of | C5⋊(C5⋊D5), #92553, #92559, … |
| Frattini subgroup of | #15691059, #15691060, #15691061, … |
| Fitting subgroup of | C52×D5, C5×C5⋊D5, C5⋊(C5⋊D5), … |
| socle of | C52×D5, C5×C5⋊D5, C5⋊(C5⋊D5), … |
| maximal subgroup of | C52×D5, C5×C5⋊D5, C5⋊(C5⋊D5), … |
| maximal normal subgroup of | C52×D5, C5×C5⋊D5, C5⋊(C5⋊D5), … |
| maximal quotient of | C2×C53, C3×C53, C52×C25, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(125, 5);
Finite Group Databasebeta