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C₂×#33526 #7622817

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

Aliases

Subgroups

4026 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

(1,2);(3,4)(5,6)(7,8)(9,15)(10,16)(11,24)(12,28)(13,18)(14,20)(17,26)(19,32)(21,34)(22,33)(23,35)(25,29)(27,38)(30,37)(31,36);(7,9)(8,14)(10,19)(11,25)(12,22)(13,21)(15,24)(16,29)(17,33)(18,31)(20,26)(23,36)(27,37)(28,30)(32,35)(34,38);(4,6)(7,9)(8,15)(10,22)(11,20)(12,19)(13,21)(14,24)(16,33)(17,29)(18,34)(23,37)(25,26)(27,36)(28,32)(30,35)(31,38);(7,10,13,12)(8,16,18,28)(9,19,21,22)(11,23,27,26)(14,29,31,30)(15,32,34,33)(17,24,35,38)(20,25,36,37)

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, 7530013);