Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1796 ⋊ C2 |
| Sylow | C53 ⋊ #22457 |
1294 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)(54,58,60,77)(55,63,65,89)(56,68,70,98)(57,72,74,105)(59,80,81,76)(61,83,84,109)(62,85,71,101)(64,91,78,88)(66,93,90,87)(67,95,97,115)(69,99,79,75)(73,107,108,104)(82,110,100,117)(86,113,102,112)(92,114,94,111)(96,116,106,103);(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)(55,62)(56,67)(58,72)(59,73)(60,74)(61,82)(63,85)(64,86)(65,71)(66,92)(68,95)(69,96)(70,97)(75,103)(76,104)(77,105)(78,102)(79,106)(80,107)(81,108)(83,110)(84,100)(87,111)(88,112)(89,101)(90,94)(91,113)(93,114)(98,115)(99,116)(109,117);(54,56,60,70)(55,61,65,84)(57,67,74,97)(58,75,77,99)(59,79,81,69)(62,82,71,100)(63,87,89,93)(64,90,78,66)(68,80,98,76)(72,103,105,116)(73,106,108,96)(83,91,109,88)(85,111,101,114)(86,94,102,92)(95,107,115,104)(110,113,117,112);(54,55)(56,66)(57,71,74,62)(58,63)(59,78)(60,65)(61,69)(64,81)(67,94,97,92)(68,93)(70,90)(72,101,105,85)(73,86,108,102)(75,109)(76,91)(77,89)(79,84)(80,88)(82,96,100,106)(83,99)(87,98)(95,111,115,114)(103,110,116,117)(104,112,107,113)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,d^b=de,e^b=eh,g^c=gh,e^d=eh,i^d=i^52806 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 185486);