Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C53×#355 ⋊ C2 |
| Sylow | C53 ⋊ #13358 |
722 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 79 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 73 points:
(2,4)(6,10)(7,14)(8,19)(11,16)(13,18)(15,20)(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);(5,7)(6,11)(8,18)(9,16)(10,14)(12,20)(13,17)(15,19)(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);(1,2)(3,4)(5,6,9,10)(7,13,16,20)(8,17,19,12)(11,18,14,15)(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)Polycyclic presentation:
2^8,53|a^2=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fgh,i^a=i^52,c^b=cf,d^b=dh,f^b=fh,g^b=gh,i^b=i^52,d^c=dg,f^c=fh,f^d=fh707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88605);