Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #25363 |
716 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 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)(54,56,57,61)(55,59,58,60)(63,71)(69,73)(70,87)(72,82)(77,88)(84,86)(85,89)(90,93);(62,65,66,79)(63,70,71,87)(64,74,75,78)(67,81,68,80)(69,84,73,86)(72,88,82,77)(76,92,83,91)(85,90,89,93);(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)(55,58)(59,60)(62,64,67,76,66,75,68,83)(63,69,72,85,71,73,82,89)(65,78,80,92,79,74,81,91)(70,86,77,90,87,84,88,93);(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)(54,55,57,58)(56,60,61,59)(62,63,68,82,66,71,67,72)(64,73,83,85,75,69,76,89)(65,77,81,70,79,88,80,87)(74,90,92,86,78,93,91,84)Polycyclic presentation:
2^8,53|a^2=ef,b^2=f,c^2=h,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^52,c^b=cg,g^b=gh,i^b=i^52,f^c=fh875 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 220010);