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C₂×#23438 #6431781

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

Aliases

Subgroups

7150 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)(9,19)(10,24)(11,16)(12,17)(13,18)(14,22)(15,27)(20,35)(21,31)(23,30)(25,32)(26,34)(28,33)(29,37)(36,38);(4,6)(7,9)(8,14)(10,25)(11,21)(12,22)(13,23)(15,32)(16,19)(17,30)(18,31)(20,26)(24,35)(27,37)(28,36)(29,33)(34,38);(7,10)(8,15)(9,20)(11,26)(12,27)(13,28)(14,29)(16,24)(17,33)(18,34)(19,32)(21,36)(22,25)(23,37)(30,38)(31,35);(7,11,13,12)(8,16,18,17)(9,21,23,22)(10,26,28,27)(14,19,31,30)(15,24,34,33)(20,36,37,25)(29,32,35,38)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338977);