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C₂×#12748 #493548

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

Aliases

Subgroups

3296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400744);