Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2264 ⋊ C2 |
| Sylow | C53 ⋊ #13671 |
284 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 55 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)(54,56)(55,62)(57,68)(58,71)(59,70)(60,72)(61,85)(63,90)(64,92)(65,91)(66,93)(67,79)(69,80)(73,88)(74,77)(75,82)(76,102)(78,84)(81,114)(83,104)(86,107)(87,97)(89,105)(94,110)(95,113)(96,115)(98,103)(99,106)(100,116)(101,112)(108,117)(109,111);(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)(55,61)(57,74)(58,69)(59,82)(60,72)(62,85)(63,95)(64,86)(65,99)(66,89)(67,73)(68,77)(70,75)(71,80)(76,108)(78,110)(79,88)(81,87)(83,103)(84,94)(90,113)(91,106)(92,107)(93,105)(96,116)(97,114)(98,104)(100,115)(101,111)(102,117)(109,112);(54,55,60,66)(56,67,72,92)(57,73,78,107)(58,79,80,64)(59,81,83,113)(61,84,89,68)(62,71,93,69)(63,94,97,77)(65,98,100,75)(70,91,104,116)(74,99,110,115)(76,85,112,105)(82,95,103,114)(86,101,88,102)(87,108,90,109)(96,111,106,117)Polycyclic presentation:
2^8,53|a^2=h,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fg,g^a=gh,d^b=df,f^b=fg,g^b=gh,e^c=eh,i^c=i^52713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90263);