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C₂²×#3116 #10575069

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

Aliases

Subgroups

8006 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)(13,14,18,22)(15,19,25,28)(16,21,17,20)(23,27,24,26);(6,9)(10,12)(13,15,18,25)(14,19,22,28)(16,23,17,24)(20,26,21,27);(14,20)(16,17)(19,26)(21,22)(23,24)(27,28);(5,7,8,11)(6,10,9,12)(13,16,18,17)(14,21,22,20)(15,23,25,24)(19,27,28,26)

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, 10482265);