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C₂×#6342377 #72334641

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

Aliases

Subgroups

79371 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((4,6)(8,10)(11,12,15,13)(14,17,18,16)(19,20,22,23)(21,25,26,24), (4,6)(7,8,9,10)(14,18)(16,17)(20,23)(21,26), (3,4)(5,6)(11,13,15,12)(14,17,18,16)(19,21,22,26)(20,24,23,25), (7,8)(9,10), (1,2), (3,4)(5,6)(7,8)(9,10)(11,14)(12,16)(13,17)(15,18)(19,20)(21,24)(22,23)(25,26));