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C₂²×#3560 #10586135

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

Aliases

Subgroups

35754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493331);