Finite Group Databasebeta

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C₂×#72232311 #72338074

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

Aliases

Subgroups

At least 23480 conjugacy classes of subgroups; only the 35560 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

284 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)(19,20)(21,23)(22,25)(24,26), (4,6)(7,8,10,9)(12,13)(14,18)(19,21,22,26)(20,23,25,24), (8,9)(11,12,15,13)(14,16,18,17)(21,26)(23,24), (8,9)(12,13)(16,17)(19,20)(21,23)(22,25)(24,26), (1,2), (4,6)(7,8,10,9)(11,13,15,12)(14,17,18,16)(19,20)(21,23)(22,25)(24,26), (3,4,5,6)(7,9,10,8)(11,14)(12,16)(13,17)(15,18)(19,21)(20,24)(22,26)(23,25));