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C₂×#11665 #481273

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

Aliases

Subgroups

970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

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

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, 388469);