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C₂×#1420727 #72299304

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

Aliases

Subgroups

70977 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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)(11,12,14,16)(13,17,18,15), (4,6)(8,10)(11,13)(12,15)(14,18)(16,17)(19,20,22,24)(21,23,25,26), (12,16)(13,18)(21,25)(23,26), (3,4)(5,6)(7,8)(9,10)(11,13)(12,17)(14,18)(15,16)(19,21)(20,23)(22,25)(24,26), (3,4)(5,6)(7,8)(9,10)(11,12)(13,17)(14,16)(15,18)(19,20)(21,23)(22,24)(25,26), (1,2));