Finite Group Databasebeta

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#34189582

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

526 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2^8,79|a^2=g,b^2=h,d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^78,c^b=cf,d^b=dg,e^b=eh,i^b=i^78,d^c=dh,e^c=egh

Conjugacy classes & character table

1516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 70881);