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#27097166

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1690 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)(57,64)(58,68)(63,78)(65,74)(67,83)(69,85)(70,79)(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)(48,51,52,49)(50,53,55,54)(58,68)(62,66)(67,83)(69,85)(76,80)(77,81)(82,87)(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)(56,59,60,71)(57,63,64,78)(58,67,68,83)(61,75,73,72)(62,76,66,80)(65,79,74,70)(69,86,85,84)(77,82,81,87);(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)(48,50,52,55)(49,53,51,54)(56,58,60,68)(57,62,64,66)(59,67,71,83)(61,69,73,85)(63,76,78,80)(65,77,74,81)(70,87,79,82)(72,84,75,86);(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)(48,49,52,51)(50,54,55,53)(56,57,60,64)(58,66,68,62)(59,70,71,79)(61,74,73,65)(63,75,78,72)(67,82,83,87)(69,77,85,81)(76,84,80,86)

Polycyclic presentation:

2^8,47|a^2=f,b^2=f,c^2=h,d^2=fh,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, 1050456);