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C₂×#13444 #499161

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

Aliases

Subgroups

1032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 406357);