Finite Group Databasebeta

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C₂²×#2984 #10574318

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

Aliases

Subgroups

7546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481514);