Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7454 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 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)(55,63,68,93)(57,71)(58,82)(59,74)(60,88)(61,72)(62,75)(64,94,97,114)(65,98,100,105)(66,101,86,91)(67,103,87,104)(69,99,106,96)(70,79)(73,89)(76,90,115,117)(77,110)(78,112)(80,111)(81,113)(83,107)(84,108)(85,109)(92,95,116,102);(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)(54,55,58,65,83,67,78,64,59,86,84,96,89,95,81,115,62,68,79,100,60,87,80,97,61,66,85,99,77,102,57,76)(56,69,71,91,110,94,109,103,72,98,111,63,88,90,70,92,75,106,113,101,73,114,108,104,74,105,112,93,107,117,82,116)Polycyclic presentation:
2^8,53|a^2=d,b^2=eg,c^2=fgh,d^2=efgh,e^2=h,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=eh,f^a=fh,i^a=i^52,c^b=cf,d^b=def,e^b=eh,f^b=fg,g^b=gh,i^b=i^521181 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57232);