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 ⋊ #8681 |
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 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:
(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)(54,56,57,63)(55,60,59,68)(58,67,65,64)(61,69,66,62)(70,73,75,86)(71,77,79,84)(72,81,83,96)(74,85,88,100)(76,89,90,98)(78,91,87,99)(80,92,93,94)(82,95,97,101);(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)(55,59)(60,68)(61,66)(62,69)(70,72,74,82,75,83,88,97)(71,76,78,80,79,90,87,93)(73,81,85,95,86,96,100,101)(77,89,91,92,84,98,99,94);(54,55)(56,62)(57,59)(58,66)(60,64)(61,65)(63,69)(67,68)(70,71)(72,80)(73,84,86,77)(74,87)(75,79)(76,82)(78,88)(81,94,96,92)(83,93)(85,91,100,99)(89,95,98,101)(90,97)Polycyclic presentation:
2^8,53|a^2=f,b^2=dgh,c^2=h,d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,e^c=egh,f^c=fg,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62804);