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C₂×#31080 #7503381

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

Aliases

Subgroups

2248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7410577);