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C₂×#33411 #7622535

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

Aliases

Subgroups

1946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529731);