Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13096 |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,57)(55,62)(56,68)(58,78)(59,81)(60,75)(61,83)(63,88)(64,91)(65,87)(66,93)(67,73)(69,101)(70,103)(71,100)(72,92)(74,82)(76,86)(77,98)(79,107)(80,99)(84,104)(85,115)(89,105)(90,114)(94,116)(95,113)(96,110)(97,111)(102,117)(106,108)(109,112);(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)(54,56,67,69,60,71,58,77)(55,61,76,95,65,85,63,66)(57,68,73,101,75,100,78,98)(59,80,96,109,82,70,79,102)(62,83,86,113,87,115,88,93)(64,90,108,94,92,84,89,111)(72,104,105,97,91,114,106,116)(74,103,107,117,81,99,110,112);(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)(54,55)(56,66,71,95)(57,72,75,91)(58,76,67,63)(59,64)(60,65)(61,69)(62,74,87,81)(68,97)(70,94,80,111)(73,106)(77,85)(78,105)(79,108,96,89)(82,92)(83,112,115,117)(84,102)(86,107)(88,110)(90,109)(93,103)(98,104,101,114)(99,113)(100,116)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^52,d^c=dh,e^c=eh,f^c=fh,f^d=fh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87129);