Finite Group Databasebeta

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C₂×#653724 #72334718

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

Aliases

Subgroups

69501 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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