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C₂×#62888 #10586223

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

Aliases

Subgroups

33806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 42 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493419);