Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C53×#1313 ⋊ C2 |
| Sylow | C53 ⋊ #11416 |
228 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 228 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) = 6784 |
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)(56,62)(59,65)(63,68)(66,69)(71,77)(76,88)(78,84)(79,90)(80,92)(89,98)(91,99)(93,96);(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)(54,56)(55,59)(57,63)(58,62)(60,66)(61,65)(64,68)(67,69)(70,72,73,82,74,83,85,97,75,81,86,94,87,95,100,101)(71,76,78,89,79,80,91,93,77,88,84,98,90,92,99,96);(54,55,57,60,58,61,64,67)(56,59,63,66,62,65,68,69)(70,71)(72,80,81,92)(73,84)(74,79)(75,77)(76,83,88,95)(78,86)(82,96,94,93)(85,99)(87,90)(89,101,98,97)(91,100)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=f,e^2=g,g^2=h,b^a=bg,c^a=ch,e^a=eh,c^b=cf,d^b=dh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78622);