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C₂×#30437 #7500750

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

Aliases

Subgroups

2825 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7407946);