Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #33470 |
632 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)(54,58,60,79)(55,63,66,65)(56,69,71,72)(57,74,77,76)(59,78,83,103)(61,85,86,94)(62,73,88,89)(64,90,93,80)(67,96,97,91)(68,99,101,102)(70,81,105,106)(75,109,82,111)(84,107,115,116)(87,108,92,112)(95,117,114,98)(100,113,104,110);(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)(54,57,58,76,60,77,79,74)(55,62,65,73,66,88,63,89)(56,68,69,102,71,101,72,99)(59,82,78,109,83,75,103,111)(61,84,94,107,86,115,85,116)(64,92,80,112,93,87,90,108)(67,95,91,117,97,114,96,98)(70,104,81,113,105,100,106,110);(54,56)(55,61)(57,68)(58,69)(59,81)(60,71)(62,84)(63,85)(64,91)(65,94)(66,86)(67,90)(70,103)(72,79)(73,107)(74,99)(75,110)(76,102)(77,101)(78,105)(80,97)(82,113)(83,106)(87,98)(88,115)(89,116)(92,117)(93,96)(95,108)(100,109)(104,111)(112,114);(54,55)(56,67,71,97)(57,73)(58,63)(59,80)(60,66)(61,70,86,105)(62,76)(64,78)(65,79)(68,98,101,117)(69,96,72,91)(74,88)(75,92)(77,89)(81,94,106,85)(82,87)(83,90)(84,110,115,113)(93,103)(95,102,114,99)(100,116,104,107)(108,111)(109,112)Polycyclic presentation:
2^8,53|a^2=f,c^2=fg,d^2=h,e^2=g,g^2=h,b^a=be,c^a=cg,e^a=eg,g^a=gh,e^b=egh,f^b=fh,g^b=gh,d^c=dh,e^c=eh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323032);