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C₂×#7984 #181238

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

Aliases

Subgroups

1838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 88434);