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C₂×#31128 #7503498

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

(1,2);(3,4,5,6)(7,8)(9,11)(10,12)(13,14)(15,16)(17,20)(18,21)(19,22)(23,30)(24,28)(25,27)(26,29);(7,9,11,8)(10,13,14,12)(15,17,18,24)(16,20,21,28)(19,23,26,25)(22,30,29,27);(4,6)(7,10,11,14)(8,12,9,13)(16,21)(17,23)(19,26)(20,27)(24,25)(28,30);(4,6)(8,9)(12,13)(16,21)(20,28)(22,29)(27,30)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7410694);