Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7480 |
166 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 166 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)(54,56,59,72,84,108,80,70,82,105,79,114,77,104,78,113,61,74,85,109,60,73,57,76,58,71,81,106,115,112,116,87)(55,62,65,89,97,107,95,69,64,88,75,111,86,100,94,101,68,92,99,110,66,90,63,93,67,91,98,102,96,117,83,103);(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)(54,55,58,64,61,68,82,67)(56,69,71,101,74,93,105,103)(57,75,78,99,80,98,116,65)(59,83,81,95,85,94,79,63)(60,86,77,66,84,96,115,97)(62,87,88,76,92,113,91,70)(72,107,106,100,109,90,114,117)(73,110,104,102,108,89,112,111)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fg,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,c^b=ch,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, 57291);