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C₂×#11112 #357701

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

Aliases

Subgroups

2718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

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, 264897);