Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C53×#1735 ⋊ C2 |
| Sylow | C53 ⋊ #23389 |
1950 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)(65,76)(69,83)(73,87)(77,89)(81,92)(84,90)(86,93)(88,91);(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)(55,57)(59,61)(62,65)(63,69)(64,73)(66,77)(67,76)(68,81)(70,84)(71,83)(72,86)(74,88)(75,87)(78,90)(79,91)(80,89)(82,92)(85,93);(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)(58,59)(60,61)(62,64,67,75)(63,68,71,82)(65,73,76,87)(66,79,80,74)(69,81,83,92)(70,85,78,72)(77,91,89,88)(84,93,90,86);(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)(56,57)(62,63,67,71)(64,72,75,85)(65,69,76,83)(66,78,80,70)(68,79,82,74)(73,86,87,93)(77,90,89,84)(81,91,92,88)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^52,c^b=cg,e^b=eh,i^b=i^52,d^c=dh,i^c=i^521508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 196395);