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C₂×#4417880 #72334449

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

Aliases

Subgroups

72307 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)(16,18)(20,23)(24,25);(7,8)(9,10)(13,17)(16,18)(19,20)(21,25)(22,23)(24,26);(4,5)(8,9)(12,15)(16,18)(21,26)(24,25);(11,12)(13,16)(14,15)(17,18)(19,20)(21,25)(22,23)(24,26);(1,2);(3,5,6,4)(7,9,10,8)(11,13)(12,16)(14,17)(15,18)(19,21,22,26)(20,24,23,25)

Conjugacy classes & character table

160 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)(16,18)(20,23)(24,25), (7,8)(9,10)(13,17)(16,18)(19,20)(21,25)(22,23)(24,26), (4,5)(8,9)(12,15)(16,18)(21,26)(24,25), (11,12)(13,16)(14,15)(17,18)(19,20)(21,25)(22,23)(24,26), (1,2), (3,5,6,4)(7,9,10,8)(11,13)(12,16)(14,17)(15,18)(19,21,22,26)(20,24,23,25));