Finite Group Databasebeta

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#27411273

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1916 conjugacy classes of subgroups; only the 287 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 85 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)(55,63)(61,77)(62,80)(64,75)(65,78)(70,81)(76,83)(79,82);(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)(54,57)(55,62)(56,66)(58,72)(59,73)(60,74)(61,76)(63,80)(64,81)(65,82)(67,71)(68,85)(69,84)(70,75)(77,83)(78,79);(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)(54,56)(55,61)(57,71)(58,68)(59,67)(60,69)(62,79)(63,77)(64,78)(65,75)(66,72)(70,76)(73,84)(74,85)(80,82)(81,83);(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)(48,49)(50,51)(52,53)(54,55)(56,65)(57,70)(58,75)(59,64)(60,63)(61,67)(62,73)(66,83)(68,77)(69,78)(71,82)(72,80)(74,81)(76,84)(79,85)

Polycyclic presentation:

2^8,53|e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,f^a=fh,i^a=i^52,c^b=cg,e^b=eh,g^b=gh,i^b=i^52,f^c=fh,g^c=gh,i^c=i^52

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 196749);