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C₂×#60100 #10574106

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

Aliases

Subgroups

10362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 38 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481302);