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#27359329

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

848 conjugacy classes of subgroups.

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

Polycyclic presentation:

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

Conjugacy classes & character table

1025 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 144805);