Finite Group Databasebeta

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C₂×#72210448 #72338055

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

Aliases

Subgroups

At least 13468 conjugacy classes of subgroups; only the 39336 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

296 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((3,4,5,6)(7,8,10,9)(12,15)(13,17)(20,22)(24,26), (11,12)(13,18)(14,15)(16,17)(19,20,23,22)(21,24,25,26), (3,4,5,6)(7,8)(9,10)(12,15)(13,17)(19,20,23,22)(21,24,25,26), (4,6)(8,9)(13,17)(16,18), (1,2), (4,6)(11,12)(13,18)(14,15)(16,17)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(7,9,10,8)(11,13)(12,16)(14,17)(15,18)(19,22,23,20)(21,24,25,26));