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C₂×#12021 #483395

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

Aliases

Subgroups

496 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)(13,22,25,37)(14,19)(15,28)(16,31)(17,21)(18,24,33,40)(20,29)(23,36,26,38)(27,35)(30,42)(32,39,34,41);(11,13,15,24,16,23,29,39,17,25,30,40,14,26,27,41)(12,18,20,22,19,34,28,38,21,33,35,37,31,32,42,36);(4,7)(8,10)(11,14,17,16)(12,19,21,31)(13,23,25,26)(15,27,30,29)(18,32,33,34)(20,28,35,42)(22,36,37,38)(24,39,40,41)

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, 390591);