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C₂×#11018 #357574

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

Aliases

Subgroups

4386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,6)(7,8,12,16,13,18,11,17)(9,19,21,14,22,29,27,30)(10,15,25,32,26,33,24,34)(20,31,35,28,36,38,23,37);(7,9)(8,14)(10,23)(11,27)(12,21)(13,22)(15,31)(16,29)(17,19)(18,30)(20,25)(24,36)(26,35)(28,32)(33,38)(34,37);(4,6)(7,10)(8,15)(9,20)(11,24)(12,25)(13,26)(14,28)(16,32)(17,34)(18,33)(19,31)(21,35)(22,36)(23,27)(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, 264770);