Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #33441 |
646 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)(55,64)(62,83)(63,86)(65,76)(66,89)(67,85)(82,105)(84,108)(87,97)(88,110)(90,102)(91,107)(92,109)(106,116)(111,114)(112,117);(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)(54,57,59,73,60,74,79,100,61,75,80,101,58,72,78,99)(55,63,66,88,65,87,90,111,64,86,89,110,76,97,102,114)(56,68,70,94,69,93,81,104,71,95,96,113,77,98,103,115)(62,82,84,106,85,107,109,117,83,105,108,116,67,91,92,112);(54,56)(55,62)(57,68)(58,77)(59,70)(60,69)(61,71)(63,82)(64,83)(65,85)(66,84)(67,76)(72,98)(73,94)(74,93)(75,95)(78,103)(79,81)(80,96)(86,105)(87,107)(88,106)(89,108)(90,109)(91,97)(92,102)(99,115)(100,104)(101,113)(110,116)(111,117)(112,114);(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)(54,55,59,66,60,65,79,90,61,64,80,89,58,76,78,102)(56,67,70,92,69,62,81,84,71,85,96,109,77,83,103,108)(57,63,73,88,74,87,100,111,75,86,101,110,72,97,99,114)(68,91,94,112,93,82,104,106,95,107,113,117,98,105,115,116)Polycyclic presentation:
2^8,53|a^2=f,c^2=f,e^2=h,f^2=g,g^2=h,b^a=be,d^a=dh,e^a=eh,i^a=i^52,e^b=eh,i^c=i^521232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322809);