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C₂×#33832 #7623579

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

Aliases

Subgroups

2028 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)(9,18,22,29)(10,23,26,32)(11,14,25,16)(13,28,31,20)(15,33,35,24)(19,36,37,30)(21,38,27,34);(7,9,12,22)(8,13,17,31)(10,19,26,37)(11,27,25,21)(14,30,16,36)(15,34,35,38)(18,32,29,23)(20,33,28,24);(4,6);(8,14)(9,19)(10,24)(11,25)(13,29)(16,17)(18,31)(20,21)(22,37)(23,32)(26,33)(27,28)(30,34)(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, 7530775);