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#34198293

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

306 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 127 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)(82,88)(85,91)(89,94)(92,95)(96,99,101,113)(97,103,106,105)(98,108,110,111)(100,112,116,126)(102,117,118,119)(104,120,122,114)(107,121,123,124)(109,125,127,115);(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)(81,85)(83,89)(84,88)(86,92)(87,91)(90,94)(93,95)(96,98)(97,102)(99,111)(100,115)(101,110)(103,119)(104,121)(105,117)(106,118)(107,120)(108,113)(109,126)(112,127)(114,123)(116,125)(122,124);(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)(80,81,83,86,84,87,90,93)(82,85,89,92,88,91,94,95)(96,97)(98,107,110,123)(99,103)(100,114)(101,106)(102,109,118,127)(104,112)(105,113)(108,121,111,124)(115,117,125,119)(116,120)(122,126)

Polycyclic presentation:

2^8,79|a^2=e,c^2=h,d^2=f,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^78,c^b=cgh,d^b=dfh,e^b=eh,f^b=fh,i^b=i^78

Conjugacy classes & character table

2230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 79592);