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#27094213

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 87 points:

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

Polycyclic presentation:

2^8,47|a^2=fh,b^2=h,d^2=h,e^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,i^a=i^46,d^b=df,e^b=eh,i^b=i^46,g^c=gh,i^c=i^46,i^d=i^46

Conjugacy classes & character table

791 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1047503);