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C₂×#32304 #7508756

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

Aliases

Subgroups

2086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7415952);