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C₄×#3111 #6373305

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

Aliases

Subgroups

2378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280501);