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C₂×#47837 #7703571

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

Aliases

Subgroups

8582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7610767);