Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13441 |
378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 121 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)(55,57)(58,61,62,77,83,112,96,114,64,80,85,78,63,79,84,113)(59,66,67,93,86,108,100,109,69,95,98,75,68,94,81,115)(60,71,72,104,87,110,117,111,74,106,88,76,73,105,82,116)(65,89,70,101,99,119,107,120,91,118,102,92,90,103,97,121);(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)(58,60,64,74)(59,65,69,91)(61,76,80,104)(62,82,85,117)(63,87,83,73)(66,92,95,101)(67,97,98,107)(68,99,86,90)(70,100,102,81)(71,77,106,78)(72,96,88,84)(75,89,93,118)(79,116,112,111)(94,121,108,120)(103,109,119,115)(105,114,110,113);(54,55)(56,57)(58,59,64,69)(60,70,74,102)(61,75,80,93)(62,81,85,100)(63,86,83,68)(65,88,91,72)(66,77,95,78)(67,96,98,84)(71,103,106,119)(73,107,87,97)(76,101,104,92)(79,115,112,109)(82,99,117,90)(89,110,118,105)(94,114,108,113)(111,120,116,121)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,c^2=d,d^2=gh,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,g^a=gh,c^b=cf,d^b=dg,e^b=eg,f^b=fg,g^b=gh,e^c=eh,f^c=fh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89117);