Finite Group Databasebeta

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C₂×#20276688 #27538025

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1130 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)(56,58)(57,63)(59,68)(60,70)(61,71)(62,64)(65,82)(66,83)(67,77)(69,74)(72,80)(73,75)(76,78)(79,87)(81,85)(84,86);(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)(57,62)(59,73)(60,69)(61,71)(63,64)(65,79)(66,81)(67,72)(68,75)(70,74)(76,86)(77,80)(78,84)(82,87)(83,85);(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)(56,57,61,66)(58,67,71,82)(59,72,76,87)(60,77,74,65)(62,78,81,68)(63,70,83,69)(64,84,85,75)(73,79,86,80);(54,55)

Conjugacy classes & character table

1502 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 323501);