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C₂×#11038 #357523

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

Aliases

Subgroups

4406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264719);