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C₂×#555905 #72332019

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

Aliases

Subgroups

84165 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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)(7,8,9,10)(12,15)(13,17)(20,23)(21,25), (19,20)(21,24)(22,23)(25,26), (1,2), (12,15)(16,18)(21,25)(24,26), (3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,16,17,18)(19,20)(21,24)(22,23)(25,26), (11,13)(12,16)(14,17)(15,18)(19,21,22,25)(20,24,23,26));