Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2239 ⋊ C2 |
| Sylow | C53 ⋊ #33658 |
534 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)(56,67)(61,83)(66,95)(68,75)(69,98)(82,113)(84,90)(85,102)(94,104)(96,107)(97,103)(99,109)(100,111)(101,112)(114,116)(115,117);(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)(54,57,59,81,60,71,77,73)(55,62,64,93,65,87,80,88)(56,66,69,103,67,95,98,97)(58,76,78,86,79,108,89,72)(61,82,85,116,83,113,102,114)(63,91,74,105,92,106,110,70)(68,100,101,107,75,111,112,96)(84,115,99,104,90,117,109,94);(54,56)(55,61)(57,66)(58,75)(59,69)(60,67)(62,82)(63,90)(64,85)(65,83)(68,79)(70,104)(71,95)(72,107)(73,97)(74,109)(76,111)(77,98)(78,112)(80,102)(81,103)(84,92)(86,96)(87,113)(88,114)(89,101)(91,117)(93,116)(94,105)(99,110)(100,108)(106,115);(54,55,60,65)(56,61,67,83)(57,70,71,105)(58,74,79,110)(59,80,77,64)(62,86,87,72)(63,89,92,78)(66,94,95,104)(68,99,75,109)(69,102,98,85)(73,91,81,106)(76,88,108,93)(82,107,113,96)(84,112,90,101)(97,115,103,117)(100,114,111,116)Polycyclic presentation:
2^8,53|a^2=h,c^2=eg,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,d^b=dh,f^b=fh,e^c=eh,f^c=fgh,g^c=gh,i^d=i^52560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324474);