Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1401 ⋊ C2 |
| Sylow | C53 ⋊ #13647 |
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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:
(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)(54,57,59,76,60,69,81,100,58,75,78,106,79,87,109,113,61,77,82,108,83,92,111,115,80,107,91,114,110,62,85,86)(55,63,65,56,66,71,95,72,67,89,96,73,98,102,116,104,68,90,97,74,99,103,117,105,64,88,93,70,94,84,112,101);(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)(55,62)(57,66)(58,73)(59,71)(60,72)(61,74)(63,85)(64,92)(65,86)(67,69)(68,87)(70,80)(75,98)(76,95)(77,99)(78,102)(79,104)(81,89)(82,103)(83,105)(84,91)(88,111)(90,109)(93,115)(94,107)(96,100)(97,113)(101,110)(106,116)(108,117)(112,114);(54,55,59,65,60,66,81,95,58,67,78,96,79,98,109,116,61,68,82,97,83,99,111,117,80,64,91,93,110,94,85,112)(56,69,71,100,72,75,89,106,73,87,102,113,104,77,90,108,74,92,103,115,105,107,88,114,70,62,84,86,101,57,63,76)Polycyclic presentation:
2^8,53|a^2=e,c^2=e,d^2=h,e^2=f,f^2=g,g^2=h,b^a=bd,d^a=dh,d^b=dh,i^c=i^521568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90129);