Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2222 ⋊ C2 |
| Sylow | C53 ⋊ #33619 |
636 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)(56,71)(62,85)(68,94)(70,100)(72,83)(73,74)(84,112)(86,87)(93,115)(95,96)(97,103)(99,116)(101,110)(102,104)(105,113)(111,117);(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)(56,70)(58,76)(59,82)(60,77)(61,78)(62,84)(64,88)(65,92)(66,75)(67,89)(68,93)(69,98)(71,100)(72,101)(73,104)(74,102)(79,106)(80,109)(81,108)(83,110)(85,112)(86,113)(87,105)(90,114)(91,107)(94,115)(95,116)(96,99)(97,117)(103,111);(54,56,69,97,60,74,81,83,61,71,80,103,59,73,58,72)(55,62,79,96,66,87,91,94,67,85,90,95,65,86,64,68)(57,70,98,117,77,102,108,110,78,100,109,111,82,104,76,101)(63,84,106,99,75,105,107,115,89,112,114,116,92,113,88,93);(54,55,61,67)(56,68,71,94)(57,75,78,92)(58,79,81,90)(59,66,60,65)(62,83,85,72)(63,82,89,77)(64,80,91,69)(70,99,100,116)(73,96,74,95)(76,107,108,88)(84,111,112,117)(86,103,87,97)(93,104,115,102)(98,106,109,114)(101,105,110,113)Polycyclic presentation:
2^8,53|a^2=h,b^2=eg,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,g^a=gh,d^b=dh,f^c=fh,i^d=i^52722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324158);