Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#1424 ⋊ C2 |
| Sylow | C53 ⋊ #13716 |
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 125 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)(54,56,57,60)(55,59,58,61)(63,70)(65,79)(66,80)(67,84)(69,87)(71,72)(73,100)(74,94)(75,101)(76,102)(77,106)(81,111)(82,95)(83,92)(85,98)(86,93)(88,89)(90,121)(91,115)(96,112)(97,99)(103,124)(104,116)(105,113)(107,119)(108,114)(109,110)(117,125)(118,120)(122,123);(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)(55,58)(59,61)(62,64,68,78)(63,69,74,91)(65,75,82,104)(66,76,85,107)(67,77,84,106)(70,87,94,115)(71,88,97,118)(72,89,99,120)(73,90,86,108)(79,101,95,116)(80,102,98,119)(81,103,109,122)(83,105,112,125)(92,113,96,117)(93,114,100,121)(110,123,111,124);(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)(56,59)(57,58)(60,61)(62,63,68,74)(64,69,78,91)(65,70,82,94)(66,83,85,112)(67,86,84,73)(71,95,97,79)(72,98,99,80)(75,87,104,115)(76,105,107,125)(77,108,106,90)(81,100,109,93)(88,116,118,101)(89,119,120,102)(92,111,96,110)(103,121,122,114)(113,124,117,123)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,c^2=d,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^52,i^b=i^52,e^c=ef,f^c=fg,g^c=gh,i^c=i^521037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90524);