Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #8477 |
682 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 131 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)(55,60)(57,66)(59,62)(63,65)(70,73)(71,77)(72,81)(74,89)(75,86)(76,91)(78,95)(79,84)(80,96)(82,99)(83,98)(85,90)(87,93)(88,97)(92,100)(94,101);(54,56,58,64)(55,59,60,62)(57,65,66,63)(61,69,68,67)(70,72,75,83)(71,76,79,92)(73,81,86,98)(74,88,90,82)(77,91,84,100)(78,94,87,80)(85,99,89,97)(93,96,95,101);(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)(54,55,57,61,58,60,66,68)(56,62,63,69,64,59,65,67)(70,71)(72,80)(73,84,86,77)(74,87)(75,79)(76,82)(78,90)(81,96,98,101)(83,94)(85,93,89,95)(88,92)(91,97,100,99)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^52,d^b=dh,e^b=eh,f^b=fgh,d^c=dh,f^c=fg1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61829);