Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#2992 ⋊ C2 |
| Sylow | C47 ⋊ #62017 |
1838 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)(48,50,51,54)(49,53,52,55)(57,63)(58,66)(62,64)(67,71);(49,52)(53,55)(58,66)(61,65)(67,71)(69,70);(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)(57,62)(60,68)(61,69)(63,64)(65,70)(67,71);(48,49)(50,53)(51,52)(54,55)(56,58,59,66)(57,61,63,65)(60,67,68,71)(62,69,64,70);(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)(49,52)(50,54)(56,57)(58,65)(59,63)(60,62)(61,66)(64,68)(67,70)(69,71)Polycyclic presentation:
2^8,47|b^2=h,e^2=fh,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,i^a=i^46,d^b=df,e^b=eh,g^c=gh,i^c=i^461061 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1063125);