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Cayley diagramC29 #10587017
Aliases
Subgroups
8283458 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 9 generators on 18 points:
(1,2);(3,4);(5,6);(7,8);(9,10);(11,12);(13,14);(15,16);(17,18)
Conjugacy classes & character table
512 conjugacy classes. The character table is too large to display.
Relationships
| center of | C28×D4, C27×C22⋊C4, C27×#120, … |
| Fitting subgroup of | #72234203, #72234204, C23×#87588 |
| socle of | #72234204, C23×#87588, C28×D4, … |
| maximal subgroup of | C28×C4, C210, C29×C3, … |
| maximal normal subgroup of | C28×C4, C210, C29×C3, … |
| maximal quotient of | C28×C4, C210, C29×C3, … |
| automorphism group of | #387, #388 |
| outer automorphism group of | #20746, #21109, #21110, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 10494213);
Finite Group Databasebeta