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C₂×#19289 #6353932

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

Aliases

Subgroups

1808 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6261128);