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C₂×#72268564 #72293993

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

Aliases

Subgroups

2744432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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