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C₂³×#383 #7625228

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

Aliases

Subgroups

14418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532424);