Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C53×#508 ⋊ C2 |
| Sylow | C53 ⋊ #33617 |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 117 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)(54,58,61,60)(55,64,67,66)(56,71,74,73)(57,76,79,78)(59,80,82,69)(62,84,86,85)(63,75,88,91)(65,81,90,89)(68,93,95,94)(70,99,102,101)(72,103,104,96)(77,107,109,97)(83,105,111,112)(87,106,108,113)(92,98,114,115)(100,116,117,110);(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)(54,57)(55,63)(56,70)(58,76)(59,77)(60,78)(61,79)(62,83)(64,75)(65,87)(66,91)(67,88)(68,92)(69,97)(71,99)(72,100)(73,101)(74,102)(80,107)(81,106)(82,109)(84,105)(85,112)(86,111)(89,113)(90,108)(93,98)(94,115)(95,114)(96,110)(103,116)(104,117);(54,56,69,96,60,73,82,104,61,74,80,103,58,71,59,72)(55,62,81,93,64,84,90,95,67,86,89,94,66,85,65,68)(57,70,97,110,78,101,109,117,79,102,107,116,76,99,77,100)(63,83,106,98,75,105,108,114,88,111,113,115,91,112,87,92);(54,55)(56,68)(57,75)(58,64)(59,81)(60,66)(61,67)(62,72)(63,78)(65,69)(70,98)(71,93)(73,94)(74,95)(76,88)(77,108)(79,91)(80,90)(82,89)(83,110)(84,103)(85,96)(86,104)(87,109)(92,101)(97,106)(99,114)(100,105)(102,115)(107,113)(111,116)(112,117)Polycyclic presentation:
2^8,53|b^2=eg,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,f^c=fh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324142);