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C₂×#12554 #492852

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

Aliases

Subgroups

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400048);