Finite Group Databasebeta

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C₂³×#52031 #72325403

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

Aliases

Subgroups

1724280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 26 points:

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

Conjugacy classes & character table

416 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((7,8)(9,10)(11,12)(13,17)(14,18)(15,16)(19,20)(21,24)(22,23)(25,26), (7,8)(9,10)(20,23)(21,25), (3,4), (5,6), (7,8,10,9)(12,16)(14,17)(19,20)(21,26)(22,23)(24,25), (1,2)(3,4)(5,6), (8,9)(11,13)(12,14)(15,18)(16,17)(19,20)(21,26)(22,23)(24,25), (7,9,10,8)(11,14)(12,13)(15,17)(16,18)(19,21,22,25)(20,24,23,26));