Finite Group Databasebeta

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C₂×#72225665 #72324473

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

Aliases

Subgroups

1118544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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