Finite Group Databasebeta

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C₂×#72232301 #72297380

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

Aliases

Subgroups

At least 25870 conjugacy classes of subgroups; only the 38352 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

308 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)(12,14)(15,16)(17,19)(18,20)(21,22), (8,10)(11,12)(13,14)(15,17)(16,19)(18,22)(20,21), (7,8)(9,10)(15,16)(17,19)(18,20)(21,22), (8,10)(16,20)(19,21), (4,6)(7,8)(9,10)(15,17)(16,19)(18,22)(20,21), (3,4)(5,6)(7,8)(9,10)(15,16)(17,21)(18,20)(19,22), (1,2));