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Cayley diagramAliases
Splittings
Subgroups
125 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 24 points:
(2,5)(3,8)(6,7)(9,11,14,10)(12,24,22,15,19,18,20,23,13,17,21,16);(1,2)(3,5)(4,7)(6,8)(9,24)(10,19)(11,21)(12,16)(13,17)(14,23)(15,22)(18,20)
Polycyclic presentation:
2^2,3,2^5|a^2=h,b^2=h,d^2=e,f^2=h,g^2=h,b^a=bd,d^a=de,d^b=de,f^c=fg,g^c=f,g^f=gh
Conjugacy classes & character table
49 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | #33925⋊C3, #33929⋊C3, #33958⋊C3, … |
| maximal normal subgroup of | #33925⋊C3, #33929⋊C3, #33958⋊C3, … |
| maximal quotient of | #22540⋊C3, SL(2,𝔽3)×#107, #33958⋊C3, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5846);
Finite Group Databasebeta