Finite Group Databasebeta

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#34185802

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

436 conjugacy classes of subgroups; only the 103 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)(80,83,85,92)(81,87,82,90)(84,93,86,91)(88,95,89,94)(96,99,102,108)(97,103,104,110)(98,106,105,111)(100,109,101,107);(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)(80,82,85,81)(83,90,92,87)(84,88,86,89)(91,94,93,95)(96,98,101,104,102,105,100,97)(99,106,107,110,108,111,109,103);(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)(80,81,86,89,85,82,84,88)(83,87,93,95,92,90,91,94)(96,97,101,105,102,104,100,98)(99,106,107,103,108,111,109,110)

Polycyclic presentation:

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

Conjugacy classes & character table

1282 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 67101);