Finite Group Databasebeta

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C₂×#45741 #7702218

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

Aliases

Subgroups

7080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7609414);