Finite Group Databasebeta

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C₂×#72232119 #72325770

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

Aliases

Subgroups

At least 22534 conjugacy classes of subgroups; only the 35496 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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