Finite Group Databasebeta

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C₂×#20275993 #27411928

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 197404);