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C₂×#36079 #7629582

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

Aliases

Subgroups

8614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536778);