Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #8527 |
656 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 131 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) = 3392 |
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)(54,57,59,58)(55,61,62,63)(56,65,66,67)(60,68,64,69)(70,73,75,86)(71,77,79,84)(72,81,83,97)(74,85,88,101)(76,89,90,98)(78,91,93,99)(80,94,92,95)(82,96,87,100);(54,56,59,66)(55,60,62,64)(57,65,58,67)(61,68,63,69)(70,72)(71,76)(73,81)(74,87)(75,83)(77,89)(78,92)(79,90)(80,93)(82,88)(84,98)(85,100)(86,97)(91,95)(94,99)(96,101);(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)(54,55,58,63,59,62,57,61)(56,64,65,69,66,60,67,68)(70,71)(72,80,83,92)(73,84,86,77)(74,78)(75,79)(76,82,90,87)(81,95)(85,99,101,91)(88,93)(89,96)(94,97)(98,100)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=gh,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,d^b=dh,f^b=fgh,f^c=fh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62110);