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C₂×#33451 #7622599

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

Aliases

Subgroups

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529795);