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C₂×#72323314 #72331956

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

Aliases

Subgroups

465080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

296 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)(11,12,14,15)(13,17,18,16)(19,20,23,25)(21,24,26,22), (7,8)(9,10)(21,26)(22,24), (19,21)(20,24)(22,25)(23,26), (1,2), (3,4,5,6)(12,15)(16,17)(20,25)(22,24), (11,12)(13,16)(14,15)(17,18)(19,20)(21,24)(22,26)(23,25), (11,13)(12,16)(14,18)(15,17)(19,22,23,24)(20,21,25,26));