Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #8635 |
320 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 320 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:
(1,2)(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)(54,56,57,63)(55,60,59,62)(58,66,65,64)(61,69,67,68)(70,73)(71,78)(72,82)(74,87)(75,90)(76,88)(77,91)(79,93)(80,94)(81,95)(83,97)(84,99)(85,98)(86,89)(92,101)(96,100);(55,59)(60,62)(61,67)(68,69)(70,72,74,83,76,85,75,84)(71,77,79,81,80,92,89,96)(73,82,87,97,88,98,90,99)(78,91,93,95,94,101,86,100);(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)(54,55,58,61,57,59,65,67)(56,62,64,69,63,60,66,68)(70,71)(72,81)(73,86,88,93)(74,89)(75,79)(76,80)(77,83)(78,87,94,90)(82,91,98,101)(84,92)(85,96)(95,97,100,99)Polycyclic presentation:
2^8,53|a^2=f,b^2=dh,c^2=h,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,e^c=eg,f^c=fgh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62582);