Finite Group Databasebeta

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C₂×#72233714 #72334668

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

Aliases

Subgroups

At least 8698 conjugacy classes of subgroups; only the 39688 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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