Finite Group Databasebeta

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#34203800

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1000 conjugacy classes of subgroups; only the 111 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)(80,83,85,95)(81,87,89,102)(82,91,93,108)(84,97,98,94)(86,99,100,111)(88,103,96,101)(90,104,105,106)(92,109,110,107);(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)(81,86)(83,91)(84,92)(85,93)(87,99)(88,90)(89,100)(94,107)(95,108)(96,105)(97,109)(98,110)(101,106)(102,111)(103,104);(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)(82,90)(83,87)(84,96,98,88)(85,89)(86,92,100,110)(91,106)(93,105)(94,103,97,101)(95,102)(99,107,111,109)(104,108)

Polycyclic presentation:

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

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, 85099);