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#34204954

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 111 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,82)(81,88)(83,97)(84,101)(85,103)(86,93)(87,104)(89,108)(90,105)(91,109)(92,95)(94,98)(96,106)(99,110)(100,111)(102,107);(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81,85,102,86,90,98,91)(82,88,103,107,93,105,94,109)(83,96,95,87,84,100,99,89)(92,104,101,111,110,108,97,106);(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(81,87,90,89)(82,92,93,110)(83,95)(84,99)(85,98)(88,105)(91,100,102,96)(94,101,103,97)(104,111)(106,108)

Polycyclic presentation:

2^8,79|a^2=f,b^2=fg,d^2=g,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,i^a=i^78,d^b=dg,e^b=eg,f^b=fh,g^b=gh,i^b=i^78,d^c=dg,e^c=egh,f^c=fh,g^c=gh

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 86253);