Finite Group Databasebeta

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C₂×#10586472 #72233488

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

Aliases

Subgroups

517593 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 18 points:

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

Conjugacy classes & character table

292 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((3,4)(5,10)(6,8)(7,9), (3,5,7,8)(4,6,9,10), (3,4)(5,10)(6,8)(7,9)(11,12)(13,16)(14,17)(15,18), (3,5,7,8)(4,6,9,10)(11,13)(12,15)(14,18)(16,17), (3,4)(5,6)(7,9)(8,10)(11,13)(12,16)(14,18)(15,17), (1,2), (11,12)(13,15)(14,17)(16,18), (3,6)(4,8)(5,9)(7,10)(11,12)(13,15)(14,17)(16,18));