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C₂×#27599 #6458776

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

Aliases

Subgroups

2194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6365972);