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C₂×#72339897 #72339992

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

Aliases

Subgroups

1102878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

344 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)(11,12)(13,14)(15,17)(16,18)(19,20)(21,24)(22,25)(23,26), (11,13,15,18)(12,16,17,14), (4,6)(8,10)(19,21,22,26)(20,23,25,24), (8,10), (11,12)(13,16)(14,18)(15,17)(19,20)(21,23)(22,25)(24,26), (3,4)(5,6)(7,8)(9,10)(11,14,15,16)(12,13,17,18)(19,21)(20,24)(22,26)(23,25), (1,2));