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C₄×#3545 #7626196

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

Aliases

Subgroups

7290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7533392);