Finite Group Databasebeta

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#27180496

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 133 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(103,110)(108,123)(109,124)(111,118)(112,126)(122,133)(125,127)(128,129);(102,105,107,117)(103,109,110,124)(104,113,115,131)(106,120,121,116)(108,122,123,133)(111,127,118,125)(112,128,126,129)(114,132,119,130);(102,104)(103,108)(105,113)(106,119)(107,115)(109,122)(110,123)(111,126)(112,118)(114,121)(116,132)(117,131)(120,130)(124,133)(125,128)(127,129);(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)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,112)(105,109)(106,118)(107,110)(108,114)(111,121)(113,129)(115,126)(116,127)(117,124)(119,123)(120,125)(122,130)(128,131)(132,133)

Polycyclic presentation:

2^7,101|c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^100,e^b=eg,f^b=fg,e^c=eg

Conjugacy classes & character table

1729 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 13874);