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#27124152

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

6624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 79 points:

(1,2)(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)(48,51,52,59)(49,55,54,61)(50,58,57,63)(53,60,56,62)(64,68,69,67)(65,72,71,77)(66,75,74,76)(70,79,73,78);(64,67,69,68)(65,72,71,77)(66,76,74,75)(70,79,73,78);(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)(49,54)(53,56)(55,61)(60,62)(64,67,69,68)(65,72,71,77)(66,75,74,76)(70,78,73,79);(50,57)(53,56)(58,63)(60,62)(65,71)(66,74)(72,77)(75,76);(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)(48,50)(49,53)(51,58)(52,57)(54,56)(55,60)(59,63)(61,62)(64,66)(65,70)(67,76)(68,75)(69,74)(71,73)(72,79)(77,78);(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)(50,56)(51,55)(52,54)(53,57)(58,62)(59,61)(60,63)(64,65)(66,73)(67,77)(68,72)(69,71)(70,74)(75,78)(76,79)

Polycyclic presentation:

2^8,47|d^2=h,e^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,i^a=i^46,c^b=cg,d^b=dh,i^b=i^46,i^d=i^46,i^f=i^46

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1077442);