Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7511 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 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)(55,61,63,66)(56,67)(62,81,82,78)(64,79,85,88)(65,80,86,89)(68,90)(69,91)(70,77)(83,104,106,101)(84,105,107,102)(87,103,109,110)(92,111)(93,99)(94,100)(108,116,117,115)(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)(54,55,56,62,57,64,68,83,58,65,69,84,71,87,92,108,59,66,70,81,72,88,93,104,74,89,94,105,95,110,112,116,60,63,67,82,73,85,90,106,75,86,91,107,96,109,111,117,76,61,77,78,97,79,99,101,98,80,100,102,113,103,114,115)Polycyclic presentation:
2^8,53|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,g^2=h,b^a=bg,d^a=dh,i^a=i^52,c^b=ch2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57375);