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C₂×#33585 #7622928

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

Aliases

Subgroups

2228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530124);