Finite Group Databasebeta

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C₂×#72232042 #72324489

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

Aliases

Subgroups

At least 6240 conjugacy classes of subgroups; only the 42216 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

356 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((7,8)(9,10)(11,12,14,16)(13,17,18,15)(19,20)(21,23)(22,25)(24,26), (7,8)(9,10)(11,12,14,16)(13,17,18,15)(19,21,22,26)(20,23,25,24), (13,18)(15,17), (7,8)(9,10)(11,12,14,16)(13,15,18,17)(19,21,22,26)(20,24,25,23), (1,2), (4,6)(8,10)(11,12)(13,15)(14,16)(17,18)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(7,8)(9,10)(11,13)(12,15)(14,18)(16,17)(19,20)(21,24)(22,25)(23,26));