Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7065 |
156 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 51 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 — 2 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)(54,56)(55,59,61,67)(57,63)(58,64)(60,62,65,68)(66,69)(70,72)(71,76,77,87)(73,81)(74,82)(75,80)(78,91,89,86)(79,88,90,98)(83,93)(84,95)(85,94)(92,100,99,97)(96,101);(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)(56,62,64,68)(57,65,66,60)(58,61)(59,63)(67,69)(70,71,73,78,74,79,84,92,75,77,83,89,85,90,96,99)(72,76,81,86,82,88,95,97,80,87,93,91,94,98,101,100)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=gh,d^2=f,f^2=h,b^a=bc,c^a=ce,e^a=eg,i^a=i^52,c^b=ch,d^b=degh,d^c=dg1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56210);