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C₂×#23403 #6431719

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

Aliases

Subgroups

7186 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)(9,18)(10,15)(11,16)(12,25)(13,17)(14,20)(19,34)(21,28)(22,31)(23,33)(24,32)(26,29)(27,37)(30,35)(36,38);(7,9)(8,14)(10,19)(11,20)(12,26)(13,21)(15,30)(16,28)(17,29)(18,25)(22,35)(23,37)(24,36)(27,32)(31,38)(33,34);(4,6)(7,10,13,24)(8,15,17,32)(9,19,21,36)(11,23,12,22)(14,27,29,30)(16,33,25,31)(18,34,28,38)(20,37,26,35);(7,11,13,12)(8,16,17,25)(9,20,21,26)(10,22,24,23)(14,28,29,18)(15,31,32,33)(19,35,36,37)(27,34,30,38)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338915);