Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#3067 ⋊ C2 |
| Sylow | C53 ⋊ #13312 |
520 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 97 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)(58,76)(59,84)(60,77)(61,78)(62,85)(64,89)(65,90)(66,74)(67,91)(68,96)(70,99)(71,75)(72,100)(73,101)(79,106)(80,108)(81,113)(82,111)(83,112)(86,115)(87,105)(88,95)(92,117)(93,116)(94,109)(97,107)(98,104)(102,114)(103,110);(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)(57,75)(58,80)(59,71)(60,72)(61,73)(63,88)(64,92)(65,86)(66,95)(67,87)(68,79)(69,77)(70,82)(74,105)(76,110)(78,100)(81,103)(83,102)(84,101)(85,90)(89,96)(91,115)(93,97)(94,104)(98,106)(99,112)(107,109)(108,111)(113,114)(116,117);(54,55)(56,68)(57,74)(58,79)(59,66)(60,65)(61,67)(62,70)(63,77)(64,82)(69,98)(71,104)(72,92)(73,97)(75,107)(76,109)(78,90)(80,95)(81,94)(83,93)(84,91)(85,114)(86,102)(87,103)(88,99)(89,112)(96,100)(101,117)(105,108)(106,111)(110,115)(113,116)Polycyclic presentation:
2^8,53|d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,c^b=cf,d^b=dg,f^b=fh,g^b=gh,i^b=i^52,e^c=eh,f^c=fh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88313);