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C₂×#9888 #206956

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

Aliases

Subgroups

1662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(3,4)(5,9)(6,7)(8,10)(11,12)(13,17)(14,18)(15,16)(19,20)(21,23,25,26)(22,24);(4,7)(8,9)(11,13,17,12,15,18,14,16)(19,21,22,25)(20,23)(24,26);(3,5,6,10)(4,8,7,9)(12,16)(13,18)(20,24)(21,25)

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, 114152);