Finite Group Databasebeta

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C₂×#72232109 #72325759

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

Aliases

Subgroups

At least 21922 conjugacy classes of subgroups; only the 36448 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

320 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)(5,6)(8,10)(11,12,14,15)(13,16,17,18)(19,20,23,24)(21,22,25,26), (3,4)(5,6)(7,8,9,10)(11,12,14,15)(13,16,17,18), (3,4)(5,6)(8,10)(12,15)(13,17)(20,24)(22,26), (4,6)(19,21)(20,22)(23,25)(24,26), (1,2), (7,8)(9,10)(11,12)(13,18)(14,15)(16,17)(19,21)(20,22)(23,25)(24,26), (3,4)(5,6)(11,13)(12,16)(14,17)(15,18)(19,22)(20,25)(21,24)(23,26));