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C₂×#30441 #7500759

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

Aliases

Subgroups

2803 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7407955);