Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2221 ⋊ C2 |
| Sylow | C53 ⋊ #13670 |
278 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 278 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:
(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)(54,56,61,70)(55,63,66,89)(57,68,76,98)(58,77,60,67)(59,69,80,99)(62,82,84,110)(64,88,81,86)(65,87,92,113)(71,97,103,115)(72,96,104,117)(73,94,78,107)(74,105,75,93)(79,100,108,112)(83,109,90,85)(91,114,106,111)(95,101,116,102);(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)(56,63)(57,72)(58,64)(59,79)(60,81)(61,66)(62,71)(65,73)(67,86)(68,96)(69,100)(70,89)(74,91)(75,106)(76,104)(77,88)(78,92)(80,108)(82,97)(83,101)(84,103)(85,95)(87,94)(90,102)(93,111)(98,117)(99,112)(105,114)(107,113)(109,116)(110,115);(55,62)(56,67)(57,71)(58,60)(59,73)(63,85)(64,90)(65,91)(66,84)(68,95)(69,99)(70,77)(72,79)(74,102)(75,101)(76,103)(78,80)(81,83)(82,86)(87,96)(88,110)(89,109)(92,106)(93,97)(98,116)(100,111)(104,108)(105,115)(112,114)(113,117)Polycyclic presentation:
2^8,53|c^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,i^b=i^52,e^c=eh713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90257);