Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7491 |
276 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 2 generators on 73 points:
(1,2,3,4)(5,7)(6,10)(8,11)(9,13)(12,19)(14,15)(16,18)(17,20)(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73);(5,6,8,12,10,7,14,16)(9,13,19,11,20,17,18,15)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=h,d^2=h,f^2=h,b^a=bc,c^a=cf,f^a=fg,g^a=gh,c^b=ch,d^b=df,f^b=fh,g^b=gh,i^b=i^52,d^c=dgh,f^c=fh,f^d=fh710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57324);