Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #11428 |
526 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 115 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)(62,65,67,78)(63,69,71,85)(64,73,75,76)(66,77,80,93)(68,81,82,83)(70,84,79,92)(72,86,87,90)(74,88,89,91);(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)(62,64,67,75)(63,68,71,82)(65,76,78,73)(66,74,80,89)(69,83,85,81)(70,72,79,87)(77,91,93,88)(84,90,92,86);(54,55,56,58,57,59,60,61)(62,63)(64,72)(65,69)(66,79,80,70)(67,71)(68,74,82,89)(73,86)(75,87)(76,90)(77,92,93,84)(78,85)(81,88,83,91)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=h,e^2=g,b^a=bd,d^a=df,f^a=fh,c^b=ch,e^b=ef,i^b=i^52,e^d=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78663);