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C₂×#18172 #6346427

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

Aliases

Subgroups

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6253623);