Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7473 |
170 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 170 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 — 2 generators on 121 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)(58,60,62,74,85,108,61,73,80,103,113,121,79,102,94,118,65,77,86,109,63,75,83,106,64,76,81,104,112,120,82,105)(59,66,68,89,95,107,93,101,88,115,78,99,87,98,84,100,71,92,97,117,69,90,67,72,70,91,96,116,114,119,111,110);(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)(54,55,56,57)(58,59)(60,72)(61,78)(62,84)(63,87)(64,88)(65,71)(66,73)(67,81)(68,94)(69,79)(70,80)(74,107)(75,89)(76,110)(77,101)(82,97)(83,96)(85,114)(86,111)(90,109)(91,118)(92,106)(93,113)(95,112)(98,104)(99,102)(100,103)(105,115)(108,117)(116,120)(119,121)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fg,e^2=fh,f^2=gh,g^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fg,g^a=gh,i^a=i^523404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57273);