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C₂×#7630502 #72314573

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

Aliases

Subgroups

308309 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((8,10)(14,21)(18,23)(20,25)(24,26), (4,6)(8,10)(13,19)(17,22)(20,25)(24,26), (1,2), (3,4)(5,6)(7,8)(9,10)(12,16)(17,22)(18,23)(24,26), (11,12)(13,17)(14,18)(15,16)(19,22)(20,24)(21,23)(25,26), (11,13)(12,17)(14,20)(15,19)(16,22)(18,24)(21,25)(23,26), (11,14,15,21)(12,18,16,23)(13,20,19,25)(17,24,22,26));