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C₂×#12569 #492876

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

Aliases

Subgroups

1658 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)(9,18)(10,15)(11,25)(12,28)(13,17)(14,20)(16,26)(19,33)(21,31)(22,37)(23,30)(24,32)(27,38)(29,35)(34,36);(7,9,11,21,10,19,24,36,13,23,27,20,12,22,26,35)(8,14,16,30,28,34,38,33,17,31,32,18,15,29,25,37);(7,10,13,12)(8,15,17,28)(9,19,23,22)(11,24,27,26)(14,29,31,34)(16,25,32,38)(18,33,30,37)(20,35,21,36)

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, 400072);