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C₂²×#2578 #7628014

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

Aliases

Subgroups

9210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535210);