Finite Group Databasebeta

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C₂×#72278661 #72278948

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

Aliases

Subgroups

At least 11800 conjugacy classes of subgroups; only the 35232 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

272 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((1,2)(12,15)(13,17)(20,23)(21,25), (8,10)(12,15)(16,18)(21,25)(24,26), (4,6)(13,17)(16,18)(19,20,22,23)(21,24,25,26), (4,6)(7,8)(9,10)(12,15)(13,17)(21,25)(24,26), (12,15)(13,17)(20,23)(21,25), (3,4,5,6)(11,12,14,15)(13,18,17,16)(19,20)(21,26)(22,23)(24,25), (11,13)(12,16)(14,17)(15,18)(19,21)(20,24)(22,25)(23,26));