Finite Group Databasebeta

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C₂×#8323171 #72298902

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

Aliases

Subgroups

At least 6192 conjugacy classes of subgroups; only the 29501 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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