Finite Group Databasebeta

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#27296591

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

330 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 125 points:

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

Polycyclic presentation:

2^8,53|a^2=h,b^2=h,c^2=g,d^2=fh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,i^a=i^52,d^b=df,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eh

Conjugacy classes & character table

1019 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 82067);