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Cayley diagramAliases
Subgroups
524 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 18 points:
(1,2);(4,7)(8,9)(11,12,14,16)(13,17,18,15);(3,4,6,7)(5,9,10,8);(11,13,14,18)(12,15,16,17);(3,5,6,10)(4,8,7,9)
Conjugacy classes & character table
50 conjugacy classes — view the full character table.
Relationships
| Fitting subgroup of | C2×#557⋊C3, #11711030, #11711034, … |
| maximal subgroup of | #8374, #8390, #8392, … |
| maximal normal subgroup of | #8374, #8390, #8392, … |
| maximal quotient of | C2×Q8×C4⋊C4, C2×#2351, C2×#2355, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2208);
Finite Group Databasebeta