Finite Group Databasebeta

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#34200150

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

214 conjugacy classes of subgroups; only the 79 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)(80,82,83,87,84,81,85,86)(89,96,99,98)(91,107)(95,111,112,116)(97,105,115,113)(100,114,118,117)(101,119)(106,110)(108,109);(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)(88,90,94,104)(89,95,99,112)(91,106,107,110)(92,103,93,102)(96,111,98,116)(97,114,115,117)(100,105,118,113)(101,109,119,108);(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)(80,81,83,86,84,82,85,87)(88,89,92,98,94,99,93,96)(90,100,102,117,104,118,103,114)(91,105,108,115,107,113,109,97)(95,110,111,101,112,106,116,119)

Polycyclic presentation:

2^8,79|a^2=e,b^2=h,c^2=ef,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cf,d^a=df,f^a=fh,i^a=i^78,d^b=dfh,e^b=eh,f^b=fh,i^b=i^78,d^c=dh

Conjugacy classes & character table

1762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 81449);