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C₂×#8139 #181823

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

Aliases

Subgroups

786 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)(13,21,24,34)(14,18)(15,19)(16,20)(17,23,29,37)(22,33,36,41)(25,30)(26,31)(27,32)(28,35,39,42)(38,40);(11,13)(12,17,20,29)(14,22)(15,23)(16,24)(18,28,31,39)(19,21,32,34)(25,35)(26,36)(27,37)(30,33,40,41)(38,42);(4,7)(8,10)(11,14,15,25,16,26,27,38)(12,18,19,30,20,31,32,40)(13,22,23,35,24,36,37,42)(17,28,21,33,29,39,34,41)

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, 89019);