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C₂×#72337223 #72339995

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

Aliases

Subgroups

921838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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