Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #13630 |
198 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 198 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)(56,68)(62,82)(67,90)(69,72)(70,93)(71,94)(81,97)(83,105)(84,106)(91,110)(92,111)(95,98)(96,113)(104,114)(107,116)(112,117);(54,56,57,69,61,68,60,72)(55,62,63,67,66,82,73,90)(58,70,74,81,78,93,77,97)(59,71,75,95,80,94,79,98)(64,83,85,91,88,105,99,110)(65,84,86,92,89,106,100,111)(76,96,101,104,103,113,102,114)(87,107,108,112,109,116,115,117);(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)(54,55,58,64,59,65,76,87,60,63,77,85,79,86,102,108,61,66,78,88,80,89,103,109,57,73,74,99,75,100,101,115)(56,67,70,91,71,92,96,112,72,82,97,105,98,106,114,116,68,90,93,110,94,111,113,117,69,62,81,83,95,84,104,107)Polycyclic presentation:
2^8,53|a^2=e,b^2=d,d^2=h,e^2=f,f^2=g,g^2=h,b^a=bd,d^a=dh,i^a=i^52,c^b=ch2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90061);