Finite Group Databasebeta

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C₂×#72280294 #72302822

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

Aliases

Subgroups

At least 11414 conjugacy classes of subgroups; only the 36184 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

344 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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