Finite Group Databasebeta

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#34207489

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

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

Polycyclic presentation:

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

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, 88788);