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C₂×#20274020 #27365211

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 79 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)(56,57)(58,63)(59,61)(60,62)(67,77)(70,75)(72,79)(73,76);(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)(58,62)(60,63)(64,66)(65,69)(67,76)(68,74)(70,79)(71,78)(72,75)(73,77);(57,60)(58,62)(61,63)(64,65,68,71)(66,72,74,79)(67,75,77,70)(69,76,78,73);(54,55)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 150687);