Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2113 ⋊ C2 |
| Sylow | C53 ⋊ #12685 |
890 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 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)(55,63)(56,69)(58,77)(59,74)(60,73)(61,75)(62,83)(64,90)(65,87)(66,86)(67,88)(68,95)(70,101)(71,99)(72,100)(76,98)(78,106)(79,104)(80,103)(81,105)(82,108)(84,110)(85,111)(89,97)(91,115)(92,113)(93,112)(94,114)(96,116)(102,109)(107,117);(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)(55,62)(57,69)(58,76)(59,79)(60,70)(61,71)(63,83)(64,89)(65,92)(66,68)(67,84)(72,81)(73,101)(74,104)(75,99)(77,98)(78,102)(80,82)(85,94)(86,95)(87,113)(88,110)(90,97)(91,96)(93,107)(100,105)(103,108)(106,109)(111,114)(112,117)(115,116);(54,55,59,65,60,66,80,93,61,67,81,94,58,64,78,91)(56,68,72,96,70,84,102,92,71,89,79,107,76,62,82,85)(57,63,74,87,73,86,103,112,75,88,105,114,77,90,106,115)(69,97,100,117,101,83,109,111,99,95,104,116,98,110,108,113)Polycyclic presentation:
2^8,53|a^2=f,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85019);