Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #10646 |
236 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 67 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)(55,61)(56,64)(57,58)(60,67)(62,63)(65,66)(70,73,74,85,75,86,88,99)(71,77,78,91,79,92,94,101)(72,81,82,97,83,84,87,98)(76,89,80,95,90,100,93,96);(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)(55,60)(57,65)(58,64)(59,66)(61,69)(62,68)(63,67)(70,72,75,83)(71,76,79,90)(73,84,86,81)(74,87,88,82)(77,89,92,100)(78,93,94,80)(85,97,99,98)(91,96,101,95);(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)(54,55,57,62,59,63,58,61)(56,60,65,68,66,67,64,69)(70,71)(72,80,83,93)(73,77)(74,78)(75,79)(76,82,90,87)(81,96,84,95)(85,91)(86,92)(88,94)(89,98,100,97)(99,101)Polycyclic presentation:
2^8,53|a^2=e,b^2=g,c^2=d,d^2=g,e^2=h,f^2=h,b^a=bd,c^a=ce,f^a=fg,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,f^b=fh,i^b=i^52,e^c=eh,f^c=fgh707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74458);