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C₂×#11084 #357753

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

Aliases

Subgroups

2730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264949);