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C₂×#10999 #357555

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

Aliases

Subgroups

4490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264751);