Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#2108 ⋊ C2 |
| Sylow | C53 ⋊ #12613 |
410 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)(54,57,58,71,59,72,74,95,60,73,75,96,76,97,98,113)(55,62,63,81,65,83,85,105,64,82,84,104,86,106,107,116)(56,67,69,91,70,92,94,112,68,90,77,99,93,111,100,114)(61,78,79,101,80,102,103,115,66,87,88,108,89,109,110,117);(54,56)(55,61,64,66)(57,67)(58,69)(59,70)(60,68)(62,78,82,87)(63,79,84,88)(65,80,86,89)(71,91)(72,92)(73,90)(74,94)(75,77)(76,93)(81,101,104,108)(83,102,106,109)(85,103,107,110)(95,112)(96,99)(97,111)(98,100)(105,115,116,117)(113,114);(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)(54,55,58,63,59,65,74,85,60,64,75,84,76,86,98,107)(56,66,69,88,70,89,94,110,68,61,77,79,93,80,100,103)(57,62,71,81,72,83,95,105,73,82,96,104,97,106,113,116)(67,87,91,108,92,109,112,117,90,78,99,101,111,102,114,115)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,e^2=g,g^2=h,b^a=bd,f^a=fh,i^a=i^52,d^b=dh2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84665);