Finite Group Databasebeta

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C₂×#793155 #72302423

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

Aliases

Subgroups

54483 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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