Finite Group Databasebeta

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C₂×#579520 #72296334

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

Aliases

Subgroups

40113 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((3,4,5,6)(7,8,9,10)(19,20)(21,25)(22,23)(24,26), (4,6)(13,17)(16,18)(21,26)(24,25), (4,6)(12,15)(16,18)(20,23)(21,26), (4,6)(11,12)(13,16)(14,15)(17,18)(19,20)(21,25)(22,23)(24,26), (3,4)(5,6)(11,13)(12,16)(14,17)(15,18)(19,21)(20,24)(22,26)(23,25), (1,2));