Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13233 |
432 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 99 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)(54,57,60,76,61,77,59,75)(55,63,81,104,66,90,65,73)(56,69,82,108,72,100,71,99)(58,74,83,109,80,107,68,96)(62,86,111,117,88,113,87,102)(64,89,85,105,78,110,91,103)(67,92,94,114,95,115,93,97)(70,98,84,112,79,106,101,116);(54,56,68,84)(55,62,85,94)(57,69,96,112)(58,79,60,82)(59,71,80,70)(61,72,83,101)(63,86,105,114)(64,67,65,87)(66,88,91,93)(73,102,89,92)(74,106,76,108)(75,99,107,98)(77,100,109,116)(78,95,81,111)(90,113,103,97)(104,117,110,115);(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)(54,55,60,65,61,66,59,81)(56,67,71,94,72,95,82,93)(57,73,76,90,77,104,75,63)(58,78,68,91,80,64,83,85)(62,84,87,79,88,101,111,70)(69,97,99,92,100,114,108,115)(74,105,96,110,107,103,109,89)(86,98,102,112,113,106,117,116)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=eh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,i^a=i^52,d^b=dg,f^b=fg,g^b=gh,f^d=fh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87928);