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C₂×#33648 #7623038

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

Aliases

Subgroups

1854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530234);