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C₂×#13385 #499009

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

Aliases

Subgroups

1098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406205);