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C₂²×#3139 #10575225

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

Aliases

Subgroups

7898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482421);