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C₂×#11180 #357933

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

Aliases

Subgroups

2538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 265129);