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C₂×#60749 #10575412

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

Aliases

Subgroups

8126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482608);