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C₂×#33750 #7623246

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

Aliases

Subgroups

1428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530442);