Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #11536 |
376 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 95 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)(54,56,58,57)(55,59,60,61)(62,65,67,78)(63,69,71,86)(64,73,75,76)(66,77,81,93)(68,82,83,84)(70,85,79,92)(72,88,87,90)(74,89,80,91);(62,64,67,75)(63,68,71,83)(65,76,78,73)(66,80,81,74)(69,84,86,82)(70,87,79,72)(77,89,93,91)(85,88,92,90);(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)(54,55,57,59,58,60,56,61)(62,63)(64,72,75,87)(65,69)(66,79,81,70)(67,71)(68,74)(73,88,76,90)(77,92,93,85)(78,86)(80,83)(82,89)(84,91)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=gh,d^2=h,e^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^52,c^b=ch,d^b=dh,e^b=efh,e^d=eh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79064);