Finite Group Databasebeta

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#27300574

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

370 conjugacy classes of subgroups; only the 147 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)(55,63)(56,68)(58,77)(59,73)(60,72)(61,74)(62,82)(64,88)(65,87)(66,89)(67,93)(69,99)(70,97)(71,98)(75,86)(76,96)(78,104)(79,101)(80,102)(81,105)(83,107)(84,108)(85,95)(90,112)(91,113)(92,111)(94,115)(100,114)(103,106)(109,117)(110,116);(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)(54,56,59,71,60,69,79,81,61,70,80,100,58,76,78,103)(55,62,65,84,64,85,90,110,66,83,91,109,75,67,92,94)(57,68,73,98,72,99,101,105,74,97,102,114,77,96,104,106)(63,82,87,108,88,95,112,116,89,107,113,117,86,93,111,115);(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)(54,55,59,65,60,64,79,90,61,66,80,91,58,75,78,92)(56,67,71,94,69,62,81,84,70,85,100,110,76,83,103,109)(57,63,73,87,72,88,101,112,74,89,102,113,77,86,104,111)(68,95,98,116,99,107,105,117,97,93,114,115,96,82,106,108)

Polycyclic presentation:

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

Conjugacy classes & character table

1208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 86050);