Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9314 |
406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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)(56,64)(60,68)(63,69)(65,66)(70,73)(71,78)(72,81)(74,89)(75,86)(76,87)(77,91)(79,96)(80,97)(82,85)(83,100)(84,88)(90,99)(92,101)(93,98)(94,95);(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)(54,56,59,64)(55,60)(57,65,58,66)(61,63)(62,68)(67,69)(70,72,74,83,76,82,75,90)(71,77,80,92,79,94,88,93)(73,85,89,99,87,81,86,100)(78,95,97,98,96,91,84,101);(54,55,58,61,59,62,57,67)(56,63,66,68,64,69,65,60)(70,71,75,80,76,79,74,88)(72,77,83,93,82,94,90,92)(73,84,86,78,87,97,89,96)(81,98,100,95,85,101,99,91)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,c^b=cg,d^b=dh,f^b=fh,i^b=i^52,e^c=eh1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66398);