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C₂×#899160 #72299205

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

Aliases

Subgroups

41069 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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