Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C47 ⋊ #60248 |
1974 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(49,52)(53,55);(57,63)(61,64)(62,71)(69,70);(56,59,60,68)(57,62,63,71)(58,65,66,67)(61,69,64,70);(56,58,60,66)(57,61,63,64)(59,67,68,65)(62,70,71,69);(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)(48,49,50,53,51,52,54,55)(56,57)(58,64)(59,62)(60,63)(61,66)(65,70)(67,69)(68,71)Polycyclic presentation:
2^8,47|a^2=g,b^2=f,c^2=f,g^2=h,b^a=bf,d^a=df,e^a=eh,i^a=i^46,c^b=cf1928 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1034543);