Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7476 |
162 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 91 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)(54,56,59,72,83,111,76,88,58,80,81,114,86,109,79,107,62,74,77,106,60,73,78,105,61,71,84,108,75,104,57,70)(55,63,66,90,97,116,95,102,87,89,113,115,85,110,64,69,68,93,99,117,67,91,98,101,65,92,96,112,94,100,82,103);(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)(54,55,58,65,62,68,61,87)(56,69,71,101,74,103,80,102)(57,66,76,96,79,99,78,113)(59,82,81,98,77,64,84,95)(60,85,75,97,83,94,86,67)(63,88,89,70,93,105,92,107)(72,110,108,91,106,100,114,116)(73,112,109,90,111,115,104,117)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fgh,d^2=h,e^2=fh,f^2=gh,g^2=h,b^a=bc,c^a=cf,e^a=efgh,f^a=fg,g^a=gh,d^b=dh,i^b=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57280);