Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2192 ⋊ C2 |
| Sylow | C53 ⋊ #33538 |
1088 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 117 points:
(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)(54,58,61,60)(55,64,67,66)(56,70,72,83)(57,74,77,76)(59,78,82,81)(62,85,87,86)(63,73,89,93)(65,79,92,91)(68,95,96,90)(69,98,101,100)(71,80,102,110)(75,105,109,108)(84,103,113,112)(88,104,106,115)(94,97,116,114)(99,107,117,111);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57)(55,63)(56,69)(58,74)(59,75)(60,76)(61,77)(62,84)(64,73)(65,88)(66,93)(67,89)(68,94)(70,98)(71,99)(72,101)(78,105)(79,104)(80,107)(81,108)(82,109)(83,100)(85,103)(86,112)(87,113)(90,114)(91,115)(92,106)(95,97)(96,116)(102,117)(110,111);(54,56)(55,62)(57,69)(58,70)(59,80)(60,83)(61,72)(63,84)(64,85)(65,90)(66,86)(67,87)(68,79)(71,81)(73,103)(74,98)(75,107)(76,100)(77,101)(78,102)(82,110)(88,114)(89,113)(91,96)(92,95)(93,112)(94,104)(97,106)(99,108)(105,117)(109,111)(115,116);(54,55)(56,68)(57,73)(58,64)(59,79)(60,66)(61,67)(62,71)(63,76)(65,81)(69,97)(70,95)(72,96)(74,89)(75,106)(77,93)(78,92)(80,85)(82,91)(83,90)(84,111)(86,110)(87,102)(88,109)(94,100)(98,116)(99,103)(101,114)(104,108)(105,115)(107,113)(112,117)Polycyclic presentation:
2^8,53|d^2=h,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,g^a=gh,e^b=eg,g^b=gh,f^c=fh,i^d=i^52644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323519);