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C₂×#72309318 #72334569

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

Aliases

Subgroups

929296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

416 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)(13,17)(16,18)(21,25)(23,26), (3,4,5,6)(7,8,9,10)(11,12,14,15)(13,18,17,16)(19,20,22,24)(21,26,25,23), (3,4)(5,6)(12,15)(16,18)(19,21)(20,23)(22,25)(24,26), (7,8)(9,10)(11,12)(13,16)(14,15)(17,18), (11,13)(12,16)(14,17)(15,18)(19,21)(20,23)(22,25)(24,26), (1,2), (3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,17)(15,18)(19,21)(20,23)(22,25)(24,26));