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C₂×#18272 #6346570

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

Aliases

Subgroups

3648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6253766);