Finite Group Databasebeta

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#34180577

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

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

Polycyclic presentation:

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

Conjugacy classes & character table

1285 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 61876);