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C₂×#45307 #7669986

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

Aliases

Subgroups

8404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7577182);