Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7399 |
238 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 39 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)(54,56,60,71)(55,61,65,85)(57,73,77,108)(58,69,79,103)(59,81,74,70)(62,86,88,112)(63,83,78,111)(64,91,87,84)(66,92,95,89)(67,96,99,76)(68,100,101,80)(72,93,106,113)(75,107,109,97)(82,104,114,90)(94,116,102,105)(98,115,117,110);(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)(56,66,68,93)(57,72)(58,78,79,63)(59,64)(60,65)(61,67,82,97)(62,75,88,109)(69,102,70,86)(71,95,101,113)(73,83,98,84)(74,87)(76,105)(77,106)(80,104,100,90)(81,112,103,94)(85,99,114,107)(89,110,92,115)(91,108,111,117)(96,116)Polycyclic presentation:
2^8,53|a^2=d,b^2=h,c^2=fh,f^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,c^b=cf,d^b=def,f^b=fh,d^c=dg,e^d=eh701 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57066);