Finite Group Databasebeta

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C₂³×#2693 #72300210

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

Aliases

Subgroups

129109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((8,10)(11,12,15,13)(14,16,18,17)(20,23)(24,25), (7,8)(9,10)(12,13)(16,17)(19,20,22,23)(21,24,26,25), (11,13,15,12)(14,16,18,17)(19,21)(20,24)(22,26)(23,25), (11,14)(12,16)(13,17)(15,18)(19,20)(21,25)(22,23)(24,26), (3,4), (5,6), (1,2)(3,4)(5,6));