Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13455 |
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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) = 6784 |
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)(54,57,58,56)(55,59,60,61)(63,69)(64,74)(65,78)(66,79)(68,81)(70,72)(71,85)(73,86)(75,89)(76,77)(80,91)(82,93)(83,92)(84,87);(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)(54,56,58,57)(55,59,60,61)(62,64)(63,68)(65,75)(66,74)(67,77)(69,84)(70,81)(71,87)(72,82)(73,83)(76,79)(78,88)(80,89)(85,92)(86,93)(90,91);(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)(54,55,58,60)(56,61,57,59)(62,63)(64,68)(65,69)(66,71)(67,73)(70,78)(72,79)(74,87)(75,84)(76,82)(77,83)(80,86)(81,88)(85,91)(89,93)(90,92)Polycyclic presentation:
2^8,53|a^2=d,b^2=d,c^2=d,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,c^b=cf,f^b=fh,i^b=i^52,e^c=eg,f^c=fh,g^c=gh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89204);