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C₂×#18258 #6346554

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

Aliases

Subgroups

4382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253750);