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C₂×#33846 #7623595

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

Aliases

Subgroups

2124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530791);