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C₂×#33748 #7623244

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

Aliases

Subgroups

1676 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)(12,16)(13,18)(14,20)(17,22)(19,26)(21,25)(23,24);(4,7)(8,10)(12,17)(16,22)(19,23)(24,26);(11,12,18,24,14,19,21,22,15,17,25,26,20,23,13,16);(3,5,6,9)(4,8,7,10)(12,17)(16,22)(19,23)(24,26)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530440);