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C₂×#11484 #480123

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

Aliases

Subgroups

1004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 387319);