Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1536 ⋊ C2 |
| Sylow | C53 ⋊ #19089 |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 101 points:
(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)(55,60)(59,68)(61,65)(62,69)(71,78)(72,82)(77,92)(79,86)(81,98)(83,87)(93,95)(99,100);(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)(55,59)(57,67)(58,63)(60,68)(61,69)(62,65)(64,66)(70,73,75,85)(71,77,78,92)(72,81,82,98)(74,88,89,84)(76,90,91,101)(79,95,86,93)(80,96,94,97)(83,100,87,99);(57,66)(61,65)(62,69)(64,67)(70,72)(71,76)(73,81)(74,87)(75,82)(77,90)(78,91)(79,94)(80,86)(83,89)(84,100)(85,98)(88,99)(92,101)(93,96)(95,97);(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)(56,62)(57,65)(58,60)(59,64)(61,66)(63,69)(67,68)(70,71,75,78)(72,80,82,94)(73,77,85,92)(74,86,89,79)(76,87,91,83)(81,97,98,96)(84,95,88,93)(90,100,101,99)Polycyclic presentation:
2^8,53|a^2=g,c^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,d^a=dh,e^a=eg,f^a=fgh,i^a=i^52,d^b=dg,e^b=eg,f^b=fh,e^c=eh,f^c=fgh,i^c=i^52707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 151705);