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C₂×#10022 #235424

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

Aliases

Subgroups

1620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 142620);