Finite Group Databasebeta

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C₂×#72236761 #72334480

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

Aliases

Subgroups

At least 8030 conjugacy classes of subgroups; only the 40632 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

320 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)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,20)(21,22)(23,25)(24,26), (7,8)(9,10)(12,15)(16,17)(19,21)(20,24)(22,25)(23,26), (4,5)(8,9)(11,12)(13,17)(14,15)(16,18)(19,22)(20,21)(23,24)(25,26), (19,21)(20,24)(22,25)(23,26), (1,2), (3,5,6,4)(7,9,10,8)(11,12)(13,17)(14,15)(16,18)(19,21)(20,22)(23,26)(24,25), (11,13)(12,16)(14,18)(15,17)(19,20)(21,24)(22,26)(23,25));