Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13551 |
214 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 159 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)(61,79)(66,89)(68,71)(69,92)(70,93)(78,95)(80,82)(81,105)(90,97)(91,112)(94,98)(96,103)(104,114)(106,107)(113,115);(54,56)(55,61,63,79)(57,71)(58,69)(59,70)(60,67)(62,82,83,80)(64,81,86,105)(65,66,87,89)(68,74)(72,98)(73,78)(75,96)(76,92)(77,93)(84,107,108,106)(85,97,109,90)(88,91,111,112)(94,100)(95,101)(99,104)(102,103)(110,115,117,113)(114,116);(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)(54,55,57,62,58,64,72,84,59,65,73,85,75,88,99,110,60,63,74,83,76,86,100,108,77,87,101,109,102,111,116,117)(56,66,68,90,69,91,94,113,70,79,95,82,96,105,114,107,67,89,71,97,92,112,98,115,93,61,78,80,103,81,104,106)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=f,f^2=g,g^2=h,b^a=bg,e^a=eh,i^a=i^52,c^b=ch,d^b=dh2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89756);