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C₂²×#2745 #7633507

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

Aliases

Subgroups

7570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540703);