Finite Group Databasebeta

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#27542244

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 117 points:

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

Polycyclic presentation:

2^8,53|a^2=h,e^2=fg,f^2=gh,g^2=h,b^a=be,e^a=ef,f^a=fg,g^a=gh,e^b=ef,f^b=fg,g^b=gh,d^c=dh,i^d=i^52

Conjugacy classes & character table

1040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 327720);