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C₂×#33541 #7622847

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

Aliases

Subgroups

3886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530043);