Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#3236 ⋊ C2 |
| Sylow | C53 ⋊ #19093 |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 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)(55,62)(56,66)(61,76)(63,70)(65,82)(67,71)(77,79)(83,84)(87,94)(92,107)(93,109)(95,102)(99,111)(106,117)(108,110)(112,116);(54,57,59,69)(55,61,62,76)(56,65,66,82)(58,72,73,68)(60,74,75,85)(63,79,70,77)(64,80,78,81)(67,84,71,83)(86,89)(87,93)(88,96)(90,104)(91,100)(92,106)(94,109)(95,111)(97,115)(98,113)(99,102)(101,105)(103,114)(107,117)(108,116)(110,112);(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)(54,56,59,66)(55,60,62,75)(57,65,69,82)(58,71,73,67)(61,74,76,85)(63,78,70,64)(68,84,72,83)(77,80,79,81)(86,88,91,98)(87,92,94,107)(89,96,100,113)(90,103,105,97)(93,106,109,117)(95,110,102,108)(99,116,111,112)(101,115,104,114);(54,55,59,62)(56,64,66,78)(57,61,69,76)(58,70,73,63)(60,71,75,67)(65,81,82,80)(68,79,72,77)(74,84,85,83)(86,87)(88,92)(89,99)(90,102)(91,94)(93,101)(95,105)(96,112)(97,110)(98,107)(100,111)(103,108)(104,109)(106,114)(113,116)(115,117)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,c^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,d^a=dh,e^a=eg,f^a=fgh,d^b=dg,e^b=eg,f^b=fh,i^b=i^52,e^c=eh,f^c=fgh707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 151745);