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C₂×#18045 #6345029

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

Aliases

Subgroups

1864 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252225);