Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2117 ⋊ C2 |
| Sylow | C53 ⋊ #12751 |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
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)(54,57,60,76)(55,62,66,87)(56,68,71,99)(58,74,81,109)(59,77,82,75)(61,83,85,113)(63,86,90,106)(64,91,65,73)(67,93,95,116)(69,97,101,117)(70,103,72,98)(78,105,89,114)(79,107,102,111)(80,110,100,108)(84,112,92,104)(88,96,94,115);(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)(54,56)(55,61)(57,68)(58,79)(59,70)(60,71)(62,83)(63,88)(64,84)(65,92)(66,85)(67,89)(69,100)(72,82)(73,104)(74,107)(75,98)(76,99)(77,103)(78,95)(80,101)(81,102)(86,96)(87,113)(90,94)(91,112)(93,114)(97,108)(105,116)(106,115)(109,111)(110,117);(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)(54,55)(56,67,71,95)(57,73,76,91)(58,78)(59,64)(60,66)(61,69,85,101)(62,75,87,77)(63,80)(65,82)(68,96)(70,94,72,88)(74,106,109,86)(79,92,102,84)(81,89)(83,111)(90,100)(93,103)(97,112)(98,116)(99,115)(104,117)(105,108,114,110)(107,113)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,d^b=dgh,f^b=fh,g^b=gh,i^b=i^52,e^c=eh,f^c=fh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85315);