Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7207 |
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:
(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)(54,56,58,68,59,69,74,92,60,70,75,93,76,94,98,112)(55,61,64,79,65,80,87,104,62,66,82,88,83,89,106,110)(57,67,72,90,73,91,97,111,71,77,95,99,96,100,113,114)(63,84,85,107,86,108,109,117,81,78,101,102,105,103,115,116);(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)(54,55,57,63,59,65,73,86,60,62,71,81,76,83,96,105)(56,66,67,84,69,89,91,108,70,61,77,78,94,80,100,103)(58,64,72,85,74,87,97,109,75,82,95,101,98,106,113,115)(68,88,90,107,92,110,111,117,93,79,99,102,112,104,114,116)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=g,e^2=g,g^2=h,b^a=bc,c^a=cf,f^a=fh,d^b=df,i^b=i^52,d^c=dh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56574);