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C₂×#8657430 #72324617

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

Aliases

Subgroups

74417 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

178 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((5,9)(8,10)(12,15)(13,17)(20,23)(21,25), (4,7)(5,9)(13,17)(16,18)(19,20)(21,26)(22,23)(24,25), (4,7)(8,10)(12,15)(13,17), (1,2), (5,9)(8,10)(12,15)(16,18)(21,25)(24,26), (3,4)(5,8)(6,7)(9,10)(11,12)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26), (3,5)(4,8)(6,9)(7,10)(11,13)(12,16)(14,17)(15,18)(19,21)(20,24)(22,25)(23,26));