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C₂×#33587 #7622930

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

Aliases

Subgroups

2120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530126);