Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11970 |
284 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 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)(55,60)(59,62)(61,68)(67,69)(70,73,77,76)(71,79,82,88)(72,84,87,92)(74,89,91,75)(78,93,96,95)(80,81,97,99)(83,94,100,98)(85,90,101,86);(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)(54,56,58,64)(55,59,60,62)(57,65,66,63)(61,69,68,67)(70,72)(71,78)(73,84)(74,90)(75,85)(76,92)(77,87)(79,93)(80,98)(81,83)(82,96)(86,91)(88,95)(89,101)(94,97)(99,100);(54,55,57,61,58,60,66,68)(56,62,63,69,64,59,65,67)(70,71,75,81,76,79,91,97,77,82,89,99,73,88,74,80)(72,83,86,96,84,98,85,93,87,100,90,78,92,94,101,95)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=h,d^2=gh,e^2=fg,g^2=h,b^a=bd,c^a=cfh,d^a=df,d^b=dg,e^b=efg,g^b=gh,i^b=i^521496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80993);