Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11643 |
288 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 103 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)(54,57,59,58)(55,61,62,67)(56,64,66,65)(60,63,68,69)(70,73,75,76)(71,78,79,85)(72,82,84,86)(74,87,89,90)(77,91,81,93)(80,94,95,98)(83,97,88,99)(92,100,96,101);(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)(54,56,59,66)(55,60,62,68)(57,65,58,64)(61,69,67,63)(70,72,75,84)(71,77,79,81)(73,86,76,82)(74,88,89,83)(78,93,85,91)(80,96,95,92)(87,97,90,99)(94,100,98,101);(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)(56,63)(57,61)(58,67)(59,62)(60,65)(64,68)(66,69)(70,71,74,80,76,78,90,94,75,79,89,95,73,85,87,98)(72,81,83,96,82,91,97,100,84,77,88,92,86,93,99,101)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=f,d^2=fh,e^2=g,g^2=h,b^a=bd,c^a=ch,d^a=df,i^a=i^52,c^b=cf,d^b=dfh,e^b=eh,i^b=i^521508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79536);