Finite Group Databasebeta

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C₂×#72241007 #72296243

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

Aliases

Subgroups

2755404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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