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C₂²×#2505 #7627913

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

Aliases

Subgroups

8994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535109);