Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1543 ⋊ C2 |
| Sylow | C53 ⋊ #8476 |
678 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 107 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:
(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)(55,60,59,62)(57,66,65,63)(61,69,67,68)(70,73,75,86)(71,77,79,84)(72,81,83,98)(74,89,90,85)(76,91,92,100)(78,95,87,93)(80,96,94,101)(82,99,88,97);(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)(55,59)(57,65)(60,62)(63,66)(70,72)(71,76)(73,81)(74,88)(75,83)(77,91)(78,94)(79,92)(80,87)(82,90)(84,100)(85,99)(86,98)(89,97)(93,96)(95,101);(54,55,57,61,58,59,65,67)(56,62,63,69,64,60,66,68)(70,71)(72,80)(73,84,86,77)(74,87)(75,79)(76,82)(78,90)(81,96,98,101)(83,94)(85,93,89,95)(88,92)(91,97,100,99)Polycyclic presentation:
2^8,53|a^2=f,c^2=g,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=eh,f^b=fgh,d^c=dh,f^c=fg,i^c=i^521028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61821);