Finite Group Databasebeta

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C₂×#20275207 #27385980

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1678 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)(56,59,62,76)(57,64,67,80)(58,69,72,85)(60,75,61,74)(63,77,78,87)(65,73,66,79)(68,82,81,86)(70,84,71,83);(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)(57,63,67,78)(59,69)(60,70)(61,71)(62,72)(64,77,80,87)(65,68,66,81)(73,82,79,86)(74,83)(75,84)(76,85);(56,57,61,65,62,67,60,66)(58,68,71,78,72,81,70,63)(59,73,75,64,76,79,74,80)(69,77,84,86,85,87,83,82);(54,55)

Conjugacy classes & character table

1202 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 171456);