Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#2952 ⋊ C2 |
| Sylow | C47 ⋊ #61197 |
2046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 87 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)(56,60,62,61)(57,66,67,65)(58,70,71,69)(59,73,74,75)(63,77,78,81)(64,72,80,79)(68,84,85,83)(76,86,87,82);(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)(50,55)(52,54)(56,60,62,61)(57,65,67,66)(58,69,71,70)(59,73,74,75)(63,77,78,81)(64,79,80,72)(68,83,85,84)(76,86,87,82);(56,59)(57,64)(58,68)(60,73)(61,75)(62,74)(63,76)(65,79)(66,72)(67,80)(69,83)(70,84)(71,85)(77,86)(78,87)(81,82);(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)(48,50)(49,52)(51,55)(53,54)(56,58,62,71)(57,63,67,78)(59,68,74,85)(60,69,61,70)(64,76,80,87)(65,77,66,81)(72,82,79,86)(73,83,75,84);(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)(48,49,51,53)(50,54,55,52)(56,57)(58,63)(59,72)(60,65)(61,66)(62,67)(64,73)(68,82)(69,77)(70,81)(71,78)(74,79)(75,80)(76,83)(84,87)(85,86)Polycyclic presentation:
2^8,47|a^2=f,b^2=h,d^2=h,e^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,i^a=i^46,d^b=df,e^b=eh,i^b=i^46,g^c=gh,i^d=i^461067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1047478);