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C₂×#11593 #481053

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

Aliases

Subgroups

1256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 388249);