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C₂×#24316 #6445404

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

Aliases

Subgroups

3488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6352600);