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C₂×#72235253 #72339352

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

Aliases

Subgroups

960520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

320 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)(19,20)(21,23)(22,24)(25,26), (3,4)(5,6)(7,8,9,10)(11,12)(13,14)(15,16)(17,18)(19,20,22,24)(21,25,26,23), (3,4,5,6)(7,8)(9,10)(13,17)(14,18)(19,20)(21,25)(22,24)(23,26), (4,6)(8,10)(12,16)(13,17), (1,2), (3,4)(5,6)(7,8)(9,10)(11,13)(12,14)(15,17)(16,18)(19,20)(21,25)(22,24)(23,26), (11,14)(12,17)(13,16)(15,18)(19,21)(20,23)(22,26)(24,25));