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C₂×#72237466 #72339347

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

Aliases

Subgroups

At least 6650 conjugacy classes of subgroups; only the 42712 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

440 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)(8,10)(13,17)(15,18)(19,20,22,24)(21,23,26,25), (3,4,5,6)(7,8,9,10)(11,12)(13,18)(14,16)(15,17)(19,21)(20,23)(22,26)(24,25), (7,8)(9,10)(11,12,14,16)(13,15,17,18)(19,20)(21,25)(22,24)(23,26), (7,8)(9,10)(11,12)(13,15)(14,16)(17,18), (1,2), (3,4)(5,6)(7,8)(9,10), (11,13)(12,15)(14,17)(16,18)(19,20)(21,25)(22,24)(23,26));