Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#350 ⋊ C2 |
| Sylow | C53 ⋊ #33340 |
1114 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)(57,73)(63,86)(69,97)(74,76)(75,101)(83,108)(87,89)(88,110)(95,111)(98,102)(99,104)(103,105)(107,116)(109,113)(112,114)(115,117);(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)(55,63)(56,69)(58,74)(59,75)(60,76)(61,73)(62,83)(64,87)(65,88)(66,89)(67,86)(68,95)(70,98)(71,99)(72,97)(77,102)(78,103)(79,104)(80,105)(81,101)(82,107)(84,109)(85,108)(90,111)(91,112)(92,113)(93,114)(94,110)(96,115)(100,116)(106,117);(54,56)(55,62)(57,69)(58,77)(59,79)(60,70)(61,72)(63,83)(64,90)(65,92)(66,68)(67,85)(71,81)(73,97)(74,102)(75,104)(76,98)(78,100)(80,82)(84,94)(86,108)(87,111)(88,113)(89,95)(91,96)(93,106)(99,101)(103,116)(105,107)(109,110)(112,115)(114,117);(54,55,59,65,60,66,80,93,61,67,81,94,58,64,78,91)(56,68,71,96,70,85,100,92,72,90,79,106,77,62,82,84)(57,63,75,88,76,89,105,114,73,86,101,110,74,87,103,112)(69,95,99,115,98,108,116,113,97,111,104,117,102,83,107,109)Polycyclic presentation:
2^8,53|a^2=f,e^2=h,f^2=g,g^2=h,b^a=be,e^b=eh,f^b=fh,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, 322272);