Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #8791 |
262 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 101 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)(54,57,58,66,59,67,65,56)(55,61,62,60,63,64,68,69)(70,73,74,85,75,86,87,100)(71,77,78,90,79,84,91,99)(72,81,82,95,83,96,97,101)(76,88,80,92,89,98,93,94);(54,56,65,67,59,66,58,57)(55,60,68,61,63,69,62,64)(70,72)(71,76,79,89)(73,81)(74,82)(75,83)(77,88,84,98)(78,80,91,93)(85,95)(86,96)(87,97)(90,92,99,94)(100,101);(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)(56,64)(57,60)(58,68)(59,63)(61,66)(62,65)(67,69)(70,71)(72,80,83,93)(73,84,86,77)(74,78)(75,79)(76,82,89,97)(81,94)(85,99,100,90)(87,91)(88,95)(92,96)(98,101)Polycyclic presentation:
2^8,53|a^2=f,b^2=eg,c^2=d,d^2=h,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,f^b=fgh,f^c=fgh2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 63253);