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C₂×#23995 #6451774

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

Aliases

Subgroups

3886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6358970);