Finite Group Databasebeta

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#34206480

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 111 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)(80,83,84,101,87,103,86,93)(81,88,90,99,92,97,89,108)(82,95,96,100,98,91,104,109)(85,102,94,107,106,110,105,111);(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)(80,82,94,108,84,104,106,97,87,98,105,99,86,96,85,88)(81,83,100,111,89,101,95,102,92,103,109,107,90,93,91,110);(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)(80,81,85,91,86,90,105,109,87,92,106,95,84,89,94,100)(82,93,97,111,96,103,108,110,98,101,88,107,104,83,99,102)

Polycyclic presentation:

2^8,79|a^2=f,b^2=df,c^2=e,d^2=h,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^78,c^b=cg,d^b=dh,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, 87779);