Finite Group Databasebeta

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#34198948

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

402 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)(81,85)(84,86)(88,91,93,104)(89,95,97,111)(90,99,101,102)(92,103,106,119)(94,107,108,109)(96,110,105,118)(98,112,113,116)(100,114,115,117);(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)(82,87)(85,86)(88,90,93,101)(89,94,97,108)(91,102,104,99)(92,100,106,115)(95,109,111,107)(96,98,105,113)(103,117,119,114)(110,116,118,112);(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)(88,89)(90,98)(91,95)(92,105,106,96)(93,97)(94,100,108,115)(99,112)(101,113)(102,116)(103,118,119,110)(104,111)(107,114,109,117)

Polycyclic presentation:

2^8,79|a^2=e,b^2=h,c^2=h,d^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^78,c^b=ch,d^b=dg,e^b=efg,i^b=i^78,e^d=eh

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 80247);