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C₂²×#3540 #10586128

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

Aliases

Subgroups

35870 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)(15,22)(16,19)(17,25)(18,21)(20,26)(23,27)(24,28);(6,9)(10,12)(13,15,18,16)(14,19,21,22)(17,23,26,24)(20,27,25,28);(5,6)(7,10)(8,9)(11,12)(13,16,18,15)(14,19,21,22)(17,24,26,23)(20,27,25,28);(5,7)(6,10)(8,11)(9,12)(13,14)(15,22)(16,19)(17,20)(18,21)(23,28)(24,27)(25,26);(13,17,18,26)(14,20,21,25)(15,23,16,24)(19,27,22,28)

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, 10493324);