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C₂×#33521 #7622811

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

Aliases

Subgroups

4002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,13,18)(9,19,22,36)(10,17,12,15)(11,24,27,32)(14,29,31,21)(16,23,34,26)(20,37,28,33)(25,35,38,30);(7,9)(8,14)(10,20)(11,25)(12,28)(13,22)(15,30)(16,33)(17,35)(18,31)(19,24)(21,26)(23,29)(27,38)(32,36)(34,37);(4,6);(7,10,13,12)(8,15,18,17)(9,20,22,28)(11,23,27,26)(14,30,31,35)(16,32,34,24)(19,33,36,37)(21,25,29,38)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530007);