Finite Group Databasebeta

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C₂×#1515117 #72324947

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

Aliases

Subgroups

41653 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

148 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((8,10)(12,15)(16,17)(21,25)(23,26), (3,4,5,6)(8,10)(11,12,14,15)(13,17,18,16), (4,6)(12,15)(13,18)(19,20,22,24)(21,26,25,23), (4,6)(7,8,9,10)(11,12)(13,17)(14,15)(16,18)(19,20)(21,23)(22,24)(25,26), (1,2), (3,4)(5,6)(11,13)(12,16)(14,18)(15,17)(19,21)(20,23)(22,25)(24,26));