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C₂×#33586 #7622929

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

Aliases

Subgroups

2132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,12,17)(9,13,18,26)(10,14,23,30)(11,24,22,16)(15,31,29,21)(19,25,32,36)(20,35,33,28)(27,38,37,34);(3,4,5,6)(7,9)(8,13)(10,19)(11,20)(12,18)(14,25)(15,27)(16,28)(17,26)(21,34)(22,33)(23,32)(24,35)(29,37)(30,36)(31,38);(8,14)(10,21)(11,22)(13,25)(15,16)(17,30)(19,34)(20,33)(23,31)(24,29)(26,36)(27,28)(32,38)(35,37);(9,18)(13,26)(19,32)(20,33)(25,36)(27,37)(28,35)(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, 7530125);