Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×M128 ⋊ C2 |
| Sylow | C53 ⋊ #7541 |
94 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)(55,62)(56,69)(57,60)(58,79)(59,80)(63,90)(64,95)(65,94)(66,98)(67,68)(70,82)(71,89)(72,75)(73,109)(74,102)(76,105)(77,84)(78,87)(81,97)(83,88)(85,86)(91,100)(92,96)(93,113)(99,108)(101,114)(103,107)(104,106)(110,116)(111,117)(112,115);(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)(54,55,57,64,61,67,60,85)(56,68,71,95,75,62,74,86)(58,78,76,111,82,91,81,113)(59,83,77,99,84,114,80,66)(63,89,92,69,94,102,115,72)(65,97,96,70,90,105,112,79)(73,108,103,88,110,98,106,101)(87,116,93,107,100,109,117,104)Polycyclic presentation:
2^8,53|a^2=d,c^2=efh,d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^52,c^b=ceh,d^b=dh,e^b=ef,f^b=fg,g^b=gh,i^b=i^522126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57459);