Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#2253 ⋊ C2 |
| Sylow | C53 ⋊ #12464 |
172 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 59 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:
(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)(54,57)(55,63)(56,70)(58,76)(59,83)(60,77)(61,79)(62,86)(64,91)(65,96)(66,92)(67,94)(68,97)(69,102)(71,104)(72,109)(73,105)(74,107)(75,95)(78,81)(80,111)(82,90)(84,93)(85,112)(87,115)(88,103)(89,114)(98,113)(99,116)(100,110)(101,117)(106,108);(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)(54,56,69,101,60,73,58,71,61,74,59,72,81,108,82,85)(55,62,65,87,66,88,64,68,67,89,80,99,84,98,95,100)(57,70,102,117,77,105,76,104,79,107,83,109,78,106,90,112)(63,86,96,115,92,103,91,97,94,114,111,116,93,113,75,110);(54,55,61,67)(56,68,74,100)(57,75)(58,80,82,65)(59,64,69,95)(60,84,81,66)(62,85,89,71)(63,90)(70,103)(72,98,101,88)(73,87,108,99)(76,94)(77,111)(78,96)(79,91)(83,92)(86,105)(93,102)(97,112)(104,110)(106,114)(107,113)(109,116)(115,117)Polycyclic presentation:
2^8,53|a^2=fg,b^2=dfh,d^2=fh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,e^c=egh,g^c=gh,i^c=i^521025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83963);