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C₂×#33523 #7622814

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

Aliases

Subgroups

3994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

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, 7530010);