Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7208 |
248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 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 — 2 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)(54,56,59,70,60,71,81,100,61,72,82,101,57,68,75,96)(55,62,65,85,63,67,88,94,66,86,80,108,73,95,102,99)(58,76,78,105,77,83,106,109,79,69,92,98,74,97,103,112)(64,84,90,110,87,93,113,115,91,111,107,117,89,104,114,116);(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)(54,55,58,64,60,63,77,87,61,66,79,91,57,73,74,89)(56,67,69,93,71,86,97,111,72,95,76,104,68,62,83,84)(59,80,78,107,81,102,106,114,82,65,92,90,75,88,103,113)(70,99,98,116,100,85,112,110,101,94,105,115,96,108,109,117)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=h,d^2=g,e^2=g,g^2=h,b^a=bc,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,d^b=dfh,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, 56578);