Finite Group Databasebeta

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C₂×#38168 #7635406

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

Aliases

Subgroups

7252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542602);