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Cayley diagramAliases
Subgroups
454 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 18 points:
(1,2);(7,8,9,10)(13,17)(15,18);(4,6)(8,10)(11,12,14,16)(13,18,17,15);(3,4)(5,6)(7,8)(9,10)(11,13)(12,15)(14,17)(16,18)
Conjugacy classes & character table
44 conjugacy classes — view the full character table.
Relationships
| Fitting subgroup of | C2×#399⋊C3, #11711134, #11711135, … |
| maximal subgroup of | #9021, #9024, #9920, … |
| maximal normal subgroup of | #9021, #9024, #9920, … |
| maximal quotient of | C2×#1439, C2×#1444, C2×#1445, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 1125);
Finite Group Databasebeta