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C₂×#10996 #357483

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

Aliases

Subgroups

4478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264679);