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C₂×#33839 #7623587

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

Aliases

Subgroups

2108 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)(9,18,19,30)(10,23,26,32)(11,14,25,16)(13,28,29,21)(15,33,35,24)(20,36,37,31)(22,38,27,34);(7,9)(8,13)(10,20)(11,27)(12,19)(14,31)(15,34)(16,36)(17,29)(18,23)(21,24)(22,25)(26,37)(28,33)(30,32)(35,38);(4,6)(9,19)(13,29)(18,30)(20,37)(21,28)(22,27)(31,36)(34,38);(8,14)(9,20)(10,24)(11,25)(13,30)(16,17)(18,29)(19,37)(21,22)(23,32)(26,33)(27,28)(31,34)(36,38)

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530783);