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C₂×#72297588 #72299484

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

Aliases

Subgroups

At least 12228 conjugacy classes of subgroups; only the 35216 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

272 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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