Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#2258 ⋊ C2 |
| Sylow | C53 ⋊ #13648 |
184 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 83 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)(54,57,59,77,60,69,84,101,61,78,85,110,87,63,90,91,62,79,86,94,88,92,102,116,58,76,82,109,83,93,108,117)(55,64,66,74,67,96,99,107,65,95,97,81,98,112,115,113,68,75,100,56,70,72,104,73,80,106,111,71,103,89,114,105);(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)(55,63)(57,70)(58,81)(59,72)(60,73)(61,71)(62,74)(64,90)(65,92)(66,91)(67,79)(68,93)(69,80)(75,108)(76,98)(77,104)(78,103)(82,112)(83,113)(84,106)(85,89)(86,96)(87,105)(88,107)(94,99)(95,102)(97,116)(100,117)(101,111)(109,115)(110,114);(54,55,59,66,60,67,84,99,61,65,85,97,87,98,90,115,62,68,86,100,88,70,102,104,58,80,82,111,83,103,108,114)(56,69,72,101,73,78,106,110,71,63,89,91,105,79,64,94,74,92,96,116,107,76,95,109,81,93,112,117,113,57,75,77)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,c^a=ch,d^a=dh,d^b=dh,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, 90135);