Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×C22⋊C32 ⋊ C2 |
| Sylow | C53 ⋊ #13554 |
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 121 points:
(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)(60,70)(65,80)(71,90)(72,91)(73,92)(81,100)(82,101)(83,102)(93,110)(94,111)(95,112)(103,115)(104,116)(105,117)(113,120)(118,121);(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)(55,57)(58,60)(59,65)(61,71)(62,72)(63,73)(64,70)(66,81)(67,82)(68,83)(69,80)(74,93)(75,94)(76,90)(77,95)(78,91)(79,92)(84,103)(85,104)(86,100)(87,105)(88,101)(89,102)(96,113)(97,110)(98,111)(99,112)(106,118)(107,115)(108,116)(109,117)(114,120)(119,121);(54,55)(56,57)(58,59,61,66,62,67,74,84,63,68,75,85,77,87,96,106,64,69,76,86,78,88,97,107,79,89,98,108,99,109,114,119)(60,65,71,81,72,82,93,103,73,83,94,104,95,105,113,118,70,80,90,100,91,101,110,115,92,102,111,116,112,117,120,121)Polycyclic presentation:
2^8,53|a^2=e,e^2=f,f^2=g,g^2=h,b^a=bd,c^b=ch,i^c=i^522192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89763);