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C₂×#11111 #357699

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

Aliases

Subgroups

2718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264895);