Finite Group Databasebeta

?

← Prev (#27538247) Next (#27538249) →

C₂×#20276734 #27538248

• supersolvable
• solvable
• monomial

Aliases

Splittings

Subgroups

1092 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 87 points:

(4,10)(7,23)(9,25)(11,30)(12,13)(14,31)(16,22)(18,28)(20,24)(26,27)(29,32)(33,34)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87);(3,5,8,17)(4,9,13,27)(6,19,21,15)(7,22,23,16)(10,25,12,26)(11,29,18,14)(20,33,24,34)(28,31,30,32)(35,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37);(3,4)(5,14)(6,18)(7,10)(8,13)(9,15)(11,21)(12,23)(16,31)(17,29)(19,27)(20,28)(22,32)(24,30)(25,33)(26,34);(1,2)

Conjugacy classes & character table

866 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 323724);