Finite Group Databasebeta

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C₂×#72233702 #72334484

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

Aliases

Subgroups

At least 16562 conjugacy classes of subgroups; only the 40160 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

308 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)(13,14)(15,16)(17,18)(19,20)(21,25)(22,23)(24,26), (4,6)(8,10)(12,15)(13,18)(20,22)(24,25), (3,4)(5,6)(7,8)(9,10)(11,13)(12,17)(14,15)(16,18)(20,22)(21,26), (19,21)(20,24)(22,25)(23,26), (1,2), (8,10)(11,14)(12,13)(15,18)(16,17)(19,21)(20,25)(22,24)(23,26), (3,4)(5,6)(7,8)(9,10)(11,15,16,12)(13,17,18,14)(19,22,23,20)(21,25,26,24));