Finite Group Databasebeta

?

← Prev (#34202044) Next (#34202046) →

#34202045

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

336 conjugacy classes of subgroups; only the 61 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)(80,82)(81,86)(83,96)(84,91)(85,92)(87,106)(88,102)(89,103)(90,98)(93,97)(94,109)(95,101)(99,108)(100,104)(105,111)(107,110);(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)(80,81,85,89)(82,86,92,103)(83,95,99,105)(84,100,97,88)(87,94,107,98)(90,106,109,110)(91,104,93,102)(96,101,108,111);(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)(82,90,92,109)(83,94)(84,97)(86,101,103,111)(87,105)(88,100)(91,96,93,108)(95,107)(98,99)(102,106,104,110)

Polycyclic presentation:

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

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, 83344);