Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11653 |
300 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 300 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:
(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)(56,62)(59,65)(63,68)(66,69)(70,73,75,87)(71,77,80,79)(72,82,84,85)(74,86,90,101)(76,91,92,96)(78,93,95,88)(81,97,98,94)(83,89,99,100);(54,56)(55,59)(57,63)(58,62)(60,66)(61,65)(64,68)(67,69)(70,72,75,84)(71,76,80,92)(73,82,87,85)(74,89,90,100)(77,91,79,96)(78,94,95,97)(81,88,98,93)(83,86,99,101);(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)(54,55,57,60,58,61,64,67)(56,59,63,66,62,65,68,69)(70,71)(72,81,84,98)(73,77)(74,88)(75,80)(76,83,92,99)(78,86)(79,87)(82,97,85,94)(89,96,100,91)(90,93)(95,101)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=h,d^2=f,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^52,c^b=cg,d^b=dfh,e^b=eh,f^b=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79578);