Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #11957 |
406 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 111 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)(55,58)(59,61);(55,58)(56,60)(62,64)(63,69)(65,79)(66,75)(67,83)(68,78)(70,87)(71,74)(72,91)(73,86)(76,81)(77,80)(82,93)(84,89)(85,88)(90,92);(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)(54,55,56,59,57,58,60,61)(62,63,66,71,67,72,81,89,68,73,82,90,80,88,65,70)(64,74,76,86,77,87,75,91,78,92,79,69,83,84,93,85)Polycyclic presentation:
2^8,53|a^2=e,d^2=gh,e^2=fg,g^2=h,b^a=bd,c^a=cf,d^a=df,i^a=i^52,d^b=dg,e^b=efg,g^b=gh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80940);