Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1419 ⋊ C2 |
| Sylow | C53 ⋊ #13700 |
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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)(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)(54,56)(55,64)(57,70)(58,77)(59,71)(60,69)(61,72)(62,80)(63,86)(65,94)(66,92)(67,91)(68,93)(73,99)(74,103)(75,98)(76,101)(78,104)(79,102)(81,105)(82,108)(83,106)(84,90)(85,107)(87,112)(88,100)(89,111)(95,116)(96,114)(97,113)(109,117)(110,115);(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)(54,55,63,83,59,66,74,82,58,65,87,109,78,95,76,85,61,68,89,110,79,97,75,84,60,67,88,96,73,81,57,62)(56,64,86,106,71,92,103,108,77,94,112,117,104,116,101,107,72,93,111,115,102,113,98,90,69,91,100,114,99,105,70,80);(55,62)(56,69)(57,63)(58,60)(59,73)(64,90)(65,84)(66,96)(67,82)(68,85)(70,100)(71,102)(72,77)(74,88)(75,87)(76,89)(78,79)(80,91)(81,83)(86,98)(92,115)(93,108)(94,107)(95,110)(97,109)(101,112)(103,111)(105,114)(106,113)(116,117)Polycyclic presentation:
2^8,53|b^2=df,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,i^b=i^52,e^c=eh,i^c=i^52722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90432);