Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #10630 |
272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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) = 3392 |
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)(55,60)(56,62)(58,65)(59,66)(63,64)(67,69)(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)(54,56,57,63)(55,59,60,67)(58,62,65,64)(61,69,68,66)(70,72)(71,76)(73,84)(74,87)(75,83)(77,89)(78,93)(79,90)(80,94)(81,86)(82,88)(85,97)(91,96)(92,100)(95,101)(98,99);(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)(56,59)(57,60)(58,61)(62,69)(63,67)(64,66)(65,68)(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=eh,b^2=h,c^2=d,d^2=g,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,f^c=fgh1028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74355);