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C₂×#33456 #7622606

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

Aliases

Subgroups

2126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529802);