Finite Group Databasebeta

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C₂³×#43095 #72300235

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

Aliases

Subgroups

1907728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

464 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((8,10)(11,12)(13,14)(15,16)(17,18), (7,8)(9,10)(12,16)(14,18)(19,20)(21,22)(23,26)(24,25), (12,16)(14,18)(19,21)(20,24)(22,26)(23,25), (11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,25)(24,26), (11,14)(12,17)(13,16)(15,18)(19,22)(20,25)(21,26)(23,24), (3,4), (5,6), (1,2)(3,4)(5,6));