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C₂×#60685 #10575303

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

Aliases

Subgroups

6830 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)(13,18)(14,26)(15,20)(16,31)(17,21)(19,29)(22,37)(23,33)(24,34)(25,40)(27,41)(28,36)(30,42)(32,39)(35,38);(4,7)(8,10)(11,13)(12,18)(14,27)(15,24)(16,25)(17,23)(19,35)(20,34)(21,33)(22,30)(26,41)(28,39)(29,38)(31,40)(32,36)(37,42);(11,14,16,29,17,30,15,28)(12,19,20,26,21,36,31,42)(13,22,25,39,23,27,24,38)(18,32,34,37,33,35,40,41);(3,5,6,9)(4,8,7,10)(13,23)(18,33)(22,27)(24,25)(32,35)(34,40)(37,41)(38,39);(11,15,17,16)(12,20,21,31)(13,24,23,25)(14,28,30,29)(18,34,33,40)(19,26,36,42)(22,38,27,39)(32,37,35,41)

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, 10482499);