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C₂×#11074 #357650

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

Aliases

Subgroups

2682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264846);