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#27304772

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

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

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 117 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)(57,73)(62,89)(66,95)(67,83)(71,101)(72,104)(75,87)(76,107)(88,115)(90,102)(96,100)(97,105)(99,116)(103,109)(106,110)(108,114);(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)(54,56)(55,61)(57,72)(58,78)(59,82)(60,68)(62,88)(63,92)(64,94)(65,84)(66,71)(67,75)(69,74)(70,79)(73,104)(76,110)(77,85)(80,112)(81,86)(83,87)(89,115)(90,116)(91,98)(93,117)(95,101)(96,109)(97,114)(99,102)(100,103)(105,108)(106,107)(111,113);(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)(54,55,60,65)(56,66,68,95)(57,71,73,101)(58,77,80,111)(59,81,79,64)(61,83,84,67)(62,87,89,75)(63,91,93,74)(69,99,98,116)(70,100,82,96)(72,92,104,117)(76,109,107,103)(78,88,112,115)(85,110,113,106)(86,97,94,105)(90,108,102,114)

Polycyclic presentation:

2^8,53|a^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,i^a=i^52,d^b=df,e^b=eh,f^b=fg,g^b=gh,i^b=i^52,d^c=dh

Conjugacy classes & character table

1175 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90248);