Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2262 ⋊ C2 |
| Sylow | C53 ⋊ #33982 |
472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 127 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 — 4 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)(56,67)(62,83)(68,91)(69,92)(70,93)(79,105)(84,108)(85,109)(86,98)(94,112)(95,113)(96,114)(97,115)(106,110)(107,111)(116,117);(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)(55,62)(57,68)(58,69)(59,70)(60,67)(61,79)(63,84)(64,85)(65,86)(66,83)(71,94)(72,95)(73,96)(74,91)(75,97)(76,93)(77,92)(78,98)(80,106)(81,107)(82,105)(87,110)(88,108)(89,109)(90,111)(99,114)(100,116)(101,112)(102,113)(103,117)(104,115);(55,61)(57,71)(58,72)(59,76)(62,79)(63,64)(65,90)(66,82)(68,94)(69,95)(70,93)(73,103)(74,101)(75,80)(77,102)(78,81)(83,105)(84,85)(86,111)(87,104)(88,89)(91,112)(92,113)(96,117)(97,106)(98,107)(99,100)(108,109)(110,115)(114,116);(54,55)(56,62)(57,61)(58,75)(59,78)(60,66)(63,71)(64,72)(65,76)(67,83)(68,79)(69,97)(70,98)(73,90)(74,82)(77,104)(80,100)(81,99)(84,94)(85,95)(86,93)(87,103)(88,101)(89,102)(91,105)(92,115)(96,111)(106,116)(107,114)(108,112)(109,113)(110,117)Polycyclic presentation:
2^8,53|e^2=fg,f^2=gh,g^2=h,b^a=be,e^a=ef,f^a=fg,g^a=gh,e^b=ef,f^b=fg,g^b=gh,d^c=dh,i^c=i^52,i^d=i^521040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327716);