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#34199205

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

324 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)(80,83,84,92)(81,86,87,95)(82,89,90,91)(85,93,88,94)(96,99,101,113,102,114,117,100)(97,104,106,105,107,115,118,124)(98,109,111,110,112,116,119,126)(103,120,121,123,122,127,125,108);(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)(83,91)(84,90)(86,94)(87,88)(89,92)(93,95)(96,98)(97,103)(99,110)(100,116)(101,119)(102,112)(104,123)(105,120)(106,125)(107,122)(108,115)(109,113)(111,117)(114,126)(118,121)(124,127);(80,81)(82,88,90,85)(83,86)(84,87)(89,94,91,93)(92,95)(96,97)(98,108)(99,105)(100,115)(101,118)(102,107)(103,110)(104,113)(106,117)(109,121)(111,127)(112,123)(114,124)(116,125)(119,120)(122,126)

Polycyclic presentation:

2^8,79|a^2=e,c^2=f,d^2=gh,f^2=h,g^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,g^a=gh,c^b=cf,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^b=i^78

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 80504);