Finite Group Databasebeta

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#34200402

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

442 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 119 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)(81,84)(83,86)(85,87)(88,90)(89,95)(91,105)(92,102)(93,103)(94,109)(96,115)(97,113)(98,114)(99,108)(100,107)(101,106)(104,117)(110,112)(111,119)(116,118);(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)(82,84)(83,85)(86,87)(89,94)(91,104)(92,106)(95,109)(96,97)(98,111)(99,112)(100,116)(101,102)(105,117)(107,118)(108,110)(113,115)(114,119);(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)(84,87)(88,89)(90,99)(91,94)(92,108)(93,98)(95,101)(96,104)(97,106)(100,112)(102,114)(103,113)(105,115)(107,111)(109,116)(110,118)(117,119)

Polycyclic presentation:

2^8,79|d^2=fh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,i^a=i^78,d^b=df,e^b=eg,f^b=fh,i^b=i^78,d^c=dg,e^c=eh

Conjugacy classes & character table

1513 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 81701);