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C₂×#4418479 #72296189

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

Aliases

Subgroups

75873 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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)(5,6)(13,17)(16,18), (4,5)(7,8,10,9)(13,17)(16,18)(19,20)(21,25)(22,23)(24,26), (8,9)(12,15)(16,18)(20,23)(21,26), (8,9)(11,12)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26), (3,5,6,4)(7,9,10,8)(11,13,14,17)(12,16,15,18)(19,21,22,26)(20,24,23,25), (1,2));