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C₂×#18156 #6346400

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

Aliases

Subgroups

3172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253596);