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C₂×#33333 #7622427

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

Aliases

Subgroups

4082 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529623);