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C₂×#11005 #357560

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

Aliases

Subgroups

4374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

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, 264756);