Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7469 |
174 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 174 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 — 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)(55,61,63,66)(57,68)(58,69)(59,70)(60,67)(62,78,81,87)(64,79,84,88)(65,80,85,89)(71,92)(72,93)(73,77)(74,94)(75,90)(76,91)(82,101,104,108)(83,102,105,109)(86,103,107,110)(95,112)(96,99)(97,100)(98,111)(106,115,116,117)(113,114);(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)(54,55,57,62,58,64,71,82,59,65,72,83,74,86,95,106,60,63,73,81,75,84,96,104,76,85,97,105,98,107,113,116)(56,66,68,87,69,88,92,108,70,89,93,109,94,110,112,117,67,61,77,78,90,79,99,101,91,80,100,102,111,103,114,115)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=f,f^2=g,g^2=h,b^a=bc,e^a=eh,c^b=ch,i^b=i^522168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57262);