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#34205475

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

498 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)(81,88)(83,99)(84,101)(85,100)(87,104)(89,109)(90,97)(91,107)(92,106)(93,102)(94,98)(95,103)(105,108)(110,111);(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)(80,82)(81,87,91,106)(83,98)(84,102)(85,103)(86,96)(88,104,107,92)(89,108,97,111)(90,110,109,105)(93,101)(94,99)(95,100);(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)(80,81,84,89,85,90,99,107,86,91,83,97,100,109,101,88)(82,92,94,105,95,108,102,106,96,104,93,110,103,111,98,87)

Polycyclic presentation:

2^8,79|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^78,d^b=dg,e^b=egh,f^b=fg,g^b=gh,i^b=i^78,d^c=dgh,e^c=egh,f^c=fgh,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, 86774);