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C₂×#33634 #7623010

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

Aliases

Subgroups

1522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530206);