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C₂×#72278229 #72296487

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

Aliases

Subgroups

At least 39562 conjugacy classes of subgroups; only the 49771 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

460 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)(13,14)(16,18)(19,20)(21,25)(22,23)(24,26), (8,10)(12,14)(15,16)(17,18)(19,20)(21,25)(22,23)(24,26), (12,14)(20,23)(24,25), (8,10)(12,14)(21,26)(24,25), (4,6)(12,14)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(19,20)(21,25)(22,23)(24,26), (1,2));