Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2151 ⋊ C2 |
| Sylow | C53 ⋊ #13198 |
410 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 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)(55,62)(56,66,67,90)(58,72)(59,73)(60,71)(61,77,78,88)(63,83)(64,84)(65,82)(68,91,92,101)(69,70,93,97)(74,89)(75,96)(76,99)(79,103,104,113)(80,81,105,95)(85,102)(86,108)(87,110)(94,98,115,107)(100,114)(106,109,117,116)(111,112);(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)(54,56,58,68,59,69,74,94,60,67,75,92,76,93,100,115)(55,61,63,79,64,80,85,106,65,78,86,104,87,105,111,117)(57,70,96,107,73,90,114,91,71,97,72,98,99,66,89,101)(62,81,108,116,84,88,112,103,82,95,83,109,110,77,102,113);(54,55,58,63,59,64,74,85,60,65,75,86,76,87,100,111)(56,61,68,79,69,80,94,106,67,78,92,104,93,105,115,117)(57,62,72,83,73,84,89,102,71,82,96,108,99,110,114,112)(66,88,91,113,70,95,98,116,90,77,101,103,97,81,107,109)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=e,f^2=g,g^2=h,b^a=bd,c^a=ce,c^b=cg,e^b=eh,i^b=i^52,d^c=dh1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87761);