Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #13728 |
238 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 75 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:
(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)(54,55,56,57)(59,66)(65,84)(67,87)(68,88)(69,83)(70,90)(76,105)(82,110)(85,112)(86,111)(89,106)(91,116)(92,117)(93,104)(103,120)(107,109);(58,60,71,94,63,74,96,114,81,102,115,121,108,119,78,99,62,73,95,118,80,101,79,100,64,75,97,113,77,98,61,72)(59,65,76,92,68,85,106,104,83,111,109,120,110,116,87,90,66,84,105,117,88,112,89,93,69,86,107,103,82,91,67,70);(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)(55,57)(58,59)(60,70)(61,76)(62,66)(63,82)(64,83)(65,72)(67,71)(68,77)(69,81)(73,90)(74,103)(75,104)(78,105)(79,109)(80,110)(84,99)(85,113)(86,114)(87,95)(88,108)(89,115)(91,94)(92,98)(93,102)(96,107)(97,106)(100,111)(101,120)(112,121)(116,118)(117,119)Polycyclic presentation:
2^8,53|b^2=df,c^2=eh,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,i^a=i^523398 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90574);