Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13556 |
290 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 143 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)(56,67)(61,66)(68,71)(69,90)(70,91)(78,84)(79,88)(80,89)(92,95)(93,96)(94,111)(101,107)(102,108)(103,110)(112,113)(115,117);(54,56)(55,61)(57,71)(58,69)(59,70)(60,67)(62,66)(63,84)(64,79)(65,80)(68,74)(72,95)(73,96)(75,94)(76,90)(77,91)(78,81)(82,88)(83,89)(85,107)(86,108)(87,103)(92,98)(93,99)(97,113)(100,111)(101,104)(102,105)(106,110)(109,117)(112,114)(115,116);(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)(54,55,57,63,58,64,72,85,59,65,73,86,75,87,97,109,60,62,74,81,76,82,98,104,77,83,99,105,100,106,114,116)(56,66,68,84,69,88,92,107,70,89,93,108,94,110,112,117,67,61,71,78,90,79,95,101,91,80,96,102,111,103,113,115)Polycyclic presentation:
2^8,53|a^2=e,e^2=f,f^2=g,g^2=h,b^a=bd,d^a=dh,i^a=i^52,c^b=ch,e^b=eh2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89772);