Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1378 ⋊ C2 |
| Sylow | C53 ⋊ #13418 |
422 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 93 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)(54,57,58,79,62,82,61,88)(55,64,65,95,69,97,68,101)(56,71,72,104,76,106,75,111)(59,85,83,80,86,81,60,87)(63,89,70,102,93,116,92,112)(66,96,67,77,98,113,84,114)(73,108,107,105,109,78,74,110)(90,94,91,115,100,103,99,117);(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)(54,56,62,76)(55,63,69,93)(57,78,82,108)(58,75,61,72)(59,74,86,107)(60,73,83,109)(64,94,97,103)(65,92,68,70)(66,99,98,91)(67,100,84,90)(71,85,106,81)(77,112,114,102)(79,105,88,110)(80,104,87,111)(89,113,116,96)(95,117,101,115);(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)(56,70)(57,77)(58,68)(59,84)(60,66)(61,65)(62,69)(63,72)(64,80)(67,86)(71,103)(73,90)(74,91)(75,93)(76,92)(78,89)(79,96)(81,101)(82,114)(83,98)(85,95)(87,97)(88,113)(94,106)(99,107)(100,109)(102,105)(104,115)(108,116)(110,112)(111,117)Polycyclic presentation:
2^8,53|b^2=h,c^2=d,d^2=h,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,f^a=fg,g^a=gh,i^a=i^52,c^b=cf,d^b=dh,e^b=eg,f^b=fgh,g^b=gh,i^b=i^52,e^c=egh,f^c=fg,g^c=gh,i^c=i^521178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88980);