Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2957 ⋊ C2 |
| Sylow | C53 ⋊ #22460 |
1286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
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)(54,58)(55,64)(56,69)(57,73)(59,81)(60,77)(61,78)(62,84)(63,87)(65,93)(66,92)(67,95)(68,97)(70,101)(71,102)(72,104)(74,107)(75,108)(76,80)(79,91)(82,106)(83,110)(85,109)(86,90)(88,113)(89,112)(94,114)(96,111)(98,116)(99,105)(100,115)(103,117);(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)(54,57,61,75)(55,63,66,72)(56,68,71,100)(58,73,78,108)(59,74,60,82)(62,83,85,103)(64,87,92,104)(65,88,79,89)(67,94,86,96)(69,97,102,115)(70,98,80,99)(76,105,101,116)(77,106,81,107)(84,110,109,117)(90,111,95,114)(91,112,93,113);(54,56)(55,62)(57,68)(58,76)(59,80)(60,70)(61,71)(63,83)(64,90)(65,86)(66,85)(67,79)(69,77)(72,103)(73,105)(74,99)(75,100)(78,101)(81,102)(82,98)(84,91)(87,111)(88,96)(89,94)(92,95)(93,109)(97,106)(104,114)(107,115)(108,116)(110,112)(113,117);(54,55,60,65,61,66,59,79)(56,67,70,62,71,86,80,85)(57,72,74,88,75,63,82,89)(58,64,77,93,78,92,81,91)(68,96,99,83,100,94,98,103)(69,95,101,84,102,90,76,109)(73,104,107,113,108,87,106,112)(97,111,105,110,115,114,116,117)Polycyclic presentation:
2^8,53|a^2=g,c^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=de,e^b=eh,g^c=gh,i^c=i^52,e^d=eh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 185514);