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C₂×#9996 #235207

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

Aliases

Subgroups

1988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 142403);