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C₂×#11560 #480504

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

Aliases

Subgroups

1574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387700);