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C₂×#33783 #7623340

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

Aliases

Subgroups

2020 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530536);