Finite Group Databasebeta

?

← Prev (#353483) Next (#353485) →

C₂×#10800 #353484

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

Aliases

Subgroups

1834 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)(9,18,21,32)(10,15)(11,16)(12,26)(13,17)(14,20,28,22)(19,31,34,38)(23,29)(24,36)(25,30)(27,33,37,35);(7,9,12,22,13,21,11,20)(8,14,16,18,17,28,26,32)(10,19,24,35,25,34,23,33)(15,27,29,31,30,37,36,38);(4,6)(7,10,11,23,13,25,12,24)(8,15,16,29,17,30,26,36)(9,19,20,33,21,34,22,35)(14,27,18,31,28,37,32,38)

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, 260680);