Finite Group Databasebeta

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C₂×#72256564 #72342828

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

Aliases

Subgroups

2759568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

368 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((12,15)(13,17), (8,10)(13,17)(16,18), (4,6)(8,10)(12,15)(16,18)(20,23)(21,25), (1,2), (12,15)(16,18), (3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,16,17,18)(19,20,22,23)(21,24,25,26), (11,13)(12,16)(14,17)(15,18)(19,21)(20,24)(22,25)(23,26));