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C₂×#33612 #7622973

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

Aliases

Subgroups

2050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530169);