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C₂×#2821 #36686

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

Aliases

Subgroups

1185 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

(1,2);(7,8,10,12)(9,11,13,14)(16,20)(21,23)(22,26)(29,30);(4,6)(9,13)(11,14)(15,16)(17,23)(18,26)(19,20)(21,25)(22,28)(24,29)(27,30);(3,4)(5,6)(7,8)(9,11)(10,12)(13,14)(15,17,19,25)(16,21,20,23)(18,27,28,24)(22,30,26,29);(7,9)(8,11)(10,13)(12,14)(15,18,19,28)(16,22,20,26)(17,24,25,27)(21,29,23,30)

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29674);