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C₂×#20944 #6371437

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

Aliases

Subgroups

6154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278633);