Finite Group Databasebeta

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C₂×#72323310 #72331972

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

Aliases

Subgroups

At least 8952 conjugacy classes of subgroups; only the 35728 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

284 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)(13,17)(16,18), (3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,16,17,18)(19,20,22,24)(21,25,26,23), (19,20)(21,23)(22,24)(25,26), (1,2), (4,6)(12,15)(16,18)(21,26)(23,25), (3,4)(5,6)(11,12)(13,16)(14,15)(17,18)(19,20)(21,25)(22,24)(23,26), (11,13)(12,16)(14,17)(15,18)(19,21,22,26)(20,23,24,25));