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C₂×#33670 #7623080

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

Aliases

Subgroups

1760 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)(11,12,14,17)(13,19,16,24)(15,18,22,25)(20,21,26,23);(4,7)(8,10)(12,17)(18,25)(19,24)(20,26);(12,18)(13,16)(15,23)(17,25)(19,20)(21,22)(24,26);(3,5,6,9)(4,8,7,10)(11,13,14,16)(12,19,17,24)(15,21,22,23)(18,26,25,20)

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, 7530276);