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C₂×#23997 #6451861

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

Aliases

Subgroups

4020 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)(7,11)(8,12)(13,20)(14,21)(15,22)(16,28)(17,30)(18,24)(19,25)(23,31)(26,34)(27,33)(29,32);(3,5,8,15)(4,9,12,22)(6,16)(7,14,19,27)(10,20)(11,21,25,33)(13,18)(17,29)(23,32)(24,28)(26,31)(30,34);(3,6)(4,10)(5,13)(7,17)(8,18)(9,20)(11,23)(12,24)(14,26)(15,16)(19,31)(21,32)(22,28)(25,30)(27,29)(33,34);(3,7)(4,11)(5,14)(6,17)(8,19)(9,21)(10,23)(12,25)(13,26)(15,27)(16,29)(18,31)(20,32)(22,33)(24,30)(28,34)

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, 6359057);