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 ⋊ #11859 |
314 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 103 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)(55,60,61,69)(56,63,64,65)(59,67,62,68)(70,73,75,87,76,88,90,74)(71,78,80,79,81,89,91,98)(72,83,85,100,86,101,92,84)(77,93,94,82,95,97,99,96);(54,56)(55,59)(57,65)(58,64)(60,68)(61,62)(63,66)(67,69)(70,72,76,86)(71,77,81,95)(73,84,88,100)(74,83,87,101)(75,92,90,85)(78,96,89,82)(79,97,98,93)(80,99,91,94);(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)(56,62,64,59)(57,60)(58,61)(63,68,65,67)(66,69)(70,71)(72,82)(73,79)(74,89)(75,91)(76,81)(77,84)(78,87)(80,90)(83,99)(85,93)(86,96)(88,98)(92,97)(94,101)(95,100)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=f,d^2=gh,f^2=h,g^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,g^a=gh,i^a=i^52,c^b=cfh,d^b=dg,e^b=efgh,f^b=fh,g^b=gh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80522);