← Prev (#3467) Next (#3469) →
Cayley diagramAliases
Subgroups
824 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 12 points:
(1,2)(3,4);(2,4);(5,6)(7,10)(8,9)(11,12);(6,9)(10,12);(5,7,8,11)(6,10,9,12)
Conjugacy classes & character table
50 conjugacy classes — view the full character table.
Relationships
| Fitting subgroup of | D4×#41⋊C3, #11711047, #11711978, … |
| maximal subgroup of | #8436, #17507, #17511, … |
| maximal normal subgroup of | #8436, #17507, #17511, … |
| maximal quotient of | C22⋊C4×#41, C4⋊C4×#41, D4×#117, … |
| outer automorphism group of | #4082, #4086, #4090, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2200);
Finite Group Databasebeta