Finite Group Databasebeta

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C₂×#618327 #72323962

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

Aliases

Subgroups

73379 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((11,12)(13,16)(14,15)(17,18), (7,8)(9,10)(13,17)(16,18)(20,23)(24,25), (4,6)(8,10)(12,15)(13,17)(19,20,22,23)(21,24,26,25), (11,13)(12,16)(14,17)(15,18)(19,20)(21,25)(22,23)(24,26), (1,2), (3,4)(5,6)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,21,22,26)(20,24,23,25));