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C₂×#7684178 #72304263

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

Aliases

Subgroups

At least 6488 conjugacy classes of subgroups; only the 32189 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

226 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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