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C₂×#23612 #6432127

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

Aliases

Subgroups

3942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339323);