Finite Group Databasebeta

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C₂×#7674647 #72330528

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

Aliases

Subgroups

127197 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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