Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #12079 |
204 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 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)(54,56,57,59,58,60,61,55)(63,70,72,83)(65,80)(69,85,87,86)(71,89,90,78)(73,91,92,88)(74,93)(79,84)(81,82);(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)(62,64,68,77)(63,69,72,87)(65,79,80,84)(66,76,67,75)(70,85,83,86)(71,88,90,91)(73,78,92,89)(74,82,93,81);(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)(54,55,57,56,58,59,61,60)(62,63,66,70,68,72,67,83)(64,73,75,91,77,92,76,88)(65,78,81,90,80,89,82,71)(69,84,86,74,87,79,85,93)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=ef,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cfg,d^a=df,f^a=fh,i^a=i^52,d^b=dfh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81535);