Finite Group Databasebeta

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#27304569

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

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

Polycyclic presentation:

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

Conjugacy classes & character table

2132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90045);