Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #11421 |
522 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 522 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) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(63,70)(69,84)(71,73)(72,86)(74,87)(85,89)(88,90)(91,93);(54,56)(55,58)(57,61)(59,60)(62,64)(63,69)(65,78)(66,80)(67,75)(68,77)(70,84)(71,87)(72,89)(73,74)(76,82)(79,92)(81,83)(85,86)(88,91)(90,93);(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)(56,60,61,58)(57,59)(62,63,66,72,67,73,81,90,68,70,82,86,65,71,79,88)(64,74,76,91,75,84,92,89,77,87,80,93,78,69,83,85)Polycyclic presentation:
2^8,53|a^2=e,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=ch,d^a=df,i^a=i^52,d^b=dh,e^b=efh1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78640);