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C₂×#60612 #10575203

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

Aliases

Subgroups

7634 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 42 points:

(1,2);(3,4)(5,8)(6,7)(9,10)(11,12)(13,23)(14,28)(15,20)(16,21)(17,22)(18,26)(19,30)(24,32)(25,34)(27,33)(29,36)(31,35)(37,40)(38,42)(39,41);(4,7)(8,10)(11,13,16,27,17,25,15,26)(12,18,20,34,22,33,21,23)(14,24,30,40,31,38,29,39)(19,32,28,41,36,42,35,37);(3,5,6,9)(4,8,7,10)(11,14,15,29,17,31,16,30)(12,19,21,35,22,36,20,28)(13,24,26,39,25,38,27,40)(18,32,23,37,33,42,34,41);(13,25)(18,33)(23,34)(24,38)(26,27)(32,42)(37,41)(39,40);(11,15,17,16)(12,20,22,21)(13,26,25,27)(14,29,31,30)(18,34,33,23)(19,28,36,35)(24,39,38,40)(32,41,42,37)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482399);