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C₂×#24978 #6447004

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

Aliases

Subgroups

2364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4)(5,9)(6,7)(8,10)(11,12)(13,15)(14,16)(17,18)(19,20,23,27)(21,28,31,25)(22,32,24,26)(29,34,30,33);(4,7)(8,9)(11,13,14,17)(12,15,16,18)(19,21)(20,25)(22,30)(23,31)(24,29)(26,33)(27,28)(32,34);(12,16)(15,18)(21,29)(22,24)(25,33)(26,32)(28,34)(30,31);(3,5,6,10)(4,8,7,9)(19,22,23,24)(20,26,27,32)(21,30,31,29)(25,33,28,34)

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, 6354200);