Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2170 ⋊ C2 |
| Sylow | C53 ⋊ #33442 |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
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)(57,72)(63,86)(68,93)(73,75)(74,97)(82,105)(87,98)(88,110)(91,107)(94,99)(95,113)(100,101)(104,115)(106,116)(111,114)(112,117);(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)(54,57,59,74,60,75,79,101,61,72,80,97,58,73,78,100)(55,63,65,88,64,87,89,111,66,86,90,110,76,98,102,114)(56,68,70,95,69,94,81,104,71,93,96,113,77,99,103,115)(62,82,83,106,84,107,108,117,85,105,109,116,67,91,92,112);(54,56)(55,62)(57,68)(58,77)(59,70)(60,69)(61,71)(63,82)(64,84)(65,83)(66,85)(67,76)(72,93)(73,99)(74,95)(75,94)(78,103)(79,81)(80,96)(86,105)(87,107)(88,106)(89,108)(90,109)(91,98)(92,102)(97,113)(100,115)(101,104)(110,116)(111,117)(112,114);(54,55,59,65,60,64,79,89,61,66,80,90,58,76,78,102)(56,67,70,92,69,62,81,83,71,84,96,108,77,85,103,109)(57,63,74,88,75,87,101,111,72,86,97,110,73,98,100,114)(68,91,95,112,94,82,104,106,93,107,113,117,99,105,115,116)Polycyclic presentation:
2^8,53|a^2=f,c^2=f,e^2=h,f^2=g,g^2=h,b^a=be,e^a=eh,e^b=eh,d^c=dh,i^d=i^521544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322811);