Finite Group Databasebeta

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C₂×#1295673 #72297028

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

Aliases

Subgroups

51557 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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)(13,17)(14,16)(15,18)(19,20)(21,23)(22,24)(25,26), (11,13)(12,15)(14,18)(16,17)(19,21)(20,23)(22,26)(24,25), (7,8,9,10)(12,16)(15,17)(20,24)(21,26), (4,6)(7,8)(9,10)(11,13)(12,15)(14,18)(16,17)(19,21)(20,25)(22,26)(23,24), (3,4)(5,6)(11,12)(13,15)(14,16)(17,18)(19,20)(21,23)(22,24)(25,26), (1,2));