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C₂×#732088 #72334458

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

Aliases

Subgroups

71201 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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