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C₂×C₄×#504 #7622416

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

Aliases

Subgroups

2502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

(1,2);(3,4,5,6);(7,8,10,14,11,15,20,26,12,16,21,27,22,28,32,36)(9,13,18,24,19,25,31,35,17,23,29,33,30,34,37,38);(7,9)(8,13)(10,18)(11,19)(12,17)(14,24)(15,25)(16,23)(20,31)(21,29)(22,30)(26,35)(27,33)(28,34)(32,37)(36,38);(9,17)(13,23)(18,29)(19,30)(24,33)(25,34)(31,37)(35,38)

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529612);