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C₂×#4308740 #72289180

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

Aliases

Subgroups

159651 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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