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C₄×#3414 #7622602

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

Aliases

Subgroups

2004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

(1,2,3,4);(5,6)(7,16)(8,14)(9,21)(10,25)(11,13)(12,18)(15,23)(17,33)(19,32)(20,30)(22,28)(24,35)(26,31)(27,34)(29,36);(5,7)(6,12)(8,17)(9,22)(10,26)(11,19)(13,27)(14,28)(15,31)(16,21)(18,23)(20,34)(24,36)(25,29)(30,33)(32,35);(6,13)(12,27)(14,25)(15,30)(16,32)(21,35)(28,29)(31,33);(5,8,11,10)(6,14,13,25)(7,17,19,26)(9,20,24,23)(12,28,27,29)(15,21,30,35)(16,33,32,31)(18,22,34,36)

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, 7529798);