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C₂×#33618 #7622989

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

Aliases

Subgroups

1956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530185);