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C₂²×#3305 #10576290

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

Aliases

Subgroups

8370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483486);