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C₂×#11438 #480007

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

Aliases

Subgroups

1574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 387203);