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C₂×#556760 #72334567

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

Aliases

Subgroups

80661 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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