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C₂×#30438 #7500752

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

Aliases

Subgroups

2723 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7407948);