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C₂×#11130 #357817

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

Aliases

Subgroups

2674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265013);