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C₂×#737656 #72296383

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

Aliases

Subgroups

60489 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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