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C₂×#60142 #10574196

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

Aliases

Subgroups

10522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 38 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481392);