Finite Group Databasebeta

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C₂×#72323385 #72332924

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

Aliases

Subgroups

At least 15034 conjugacy classes of subgroups; only the 35736 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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