Finite Group Databasebeta

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C₂×#72232048 #72324476

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

Aliases

Subgroups

2566784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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