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C₂×#31382 #7504588

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

Aliases

Subgroups

2876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 7411784);