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C₂²×#36429 #72315144

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

Aliases

Subgroups

316537 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 20 points:

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

Conjugacy classes & character table

280 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((6,8)(9,10,12,11)(13,14)(15,19)(16,20)(17,18), (6,8)(9,10,12,11)(14,17)(19,20), (3,4)(6,8)(9,11,12,10)(13,15,18,16)(14,19,17,20), (1,2)(3,4), (10,11), (6,8)(9,10,12,11)(13,16,18,15)(14,20,17,19), (5,6,7,8)(9,11,12,10)(13,17,18,14)(15,19,16,20));