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C₂×#2381 #34345

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

Aliases

Subgroups

1163 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27333);