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C₂×#60167 #10574157

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

Aliases

Subgroups

10490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10481353);