Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C53 ⋊ #36701 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D53 |
| commutator, socle, prime radical, cosocle | C23×C53 | C25 |
| Fitting | C53×#2822 | C2 |
| hypercenter | #2822 | D53 |
| hypocenter | C53 | #36701 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #2822 | |
1304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 5 generators on 93 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)(54,56,57,60)(55,59,58,61)(78,82,83,81)(79,85,86,91)(80,88,90,89)(84,93,87,92);(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)(63,69)(65,73)(67,75)(70,72)(78,81,83,82)(79,85,86,91)(80,89,90,88)(84,93,87,92);(55,58)(59,61)(62,65)(63,68)(64,70)(66,73)(67,74)(69,77)(71,72)(75,76)(78,81,83,82)(79,85,86,91)(80,88,90,89)(84,92,87,93);(62,64,66,71)(63,67,69,75)(65,72,73,70)(68,76,77,74)(78,80,83,90)(79,84,86,87)(81,89,82,88)(85,93,91,92);(54,55)(56,59)(57,58)(60,61)(62,63,66,69)(64,67,71,75)(65,68,73,77)(70,74,72,76)(78,79,83,86)(80,87,90,84)(81,91,82,85)(88,92,89,93)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,c^2=f,d^2=f,e^2=g,b^a=bf,c^a=cg,d^a=dh,c^b=ch,d^c=dfh,i^e=i^52728 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 376289);