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C₂×#21628 #6373194

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

Aliases

Subgroups

2128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280390);