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C₂×#3069124 #72294523

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

Aliases

Subgroups

40585 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

148 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((7,8)(9,10)(11,12,15,16)(13,14,17,18)(19,20)(21,23)(22,24)(25,26), (8,10)(13,17)(14,18)(19,21,22,25)(20,23,24,26), (4,6)(12,16)(14,18)(19,20,22,24)(21,23,25,26), (11,13,15,17)(12,14,16,18)(19,20)(21,23)(22,24)(25,26), (3,4)(5,6)(7,8)(9,10)(11,14)(12,13)(15,18)(16,17)(19,21)(20,23)(22,25)(24,26), (1,2));