Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#2923 ⋊ C2 |
| Sylow | C47 ⋊ #61018 |
1672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 95 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)(48,51,52,59)(49,55,54,61)(50,58,57,63)(53,60,56,62)(68,82)(73,89)(76,81)(79,93)(85,88)(86,95)(90,92)(91,94);(49,54)(53,56)(55,61)(60,62)(64,68)(65,73)(66,76)(67,79)(69,81)(70,82)(71,85)(72,86)(74,89)(75,90)(77,91)(78,92)(80,93)(83,88)(84,94)(87,95);(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)(50,57)(53,56)(58,63)(60,62)(64,67,70,80)(65,72,74,87)(66,75,69,78)(68,79,82,93)(71,84,83,77)(73,86,89,95)(76,90,81,92)(85,94,88,91);(48,50)(49,53)(51,58)(52,57)(54,56)(55,60)(59,63)(61,62)(64,66,70,69)(65,71,74,83)(67,78,80,75)(68,81,82,76)(72,77,87,84)(73,88,89,85)(79,90,93,92)(86,94,95,91);(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)(50,56)(51,55)(52,54)(53,57)(58,62)(59,61)(60,63)(64,65)(66,71)(67,77)(68,73)(69,83)(70,74)(72,75)(76,85)(78,87)(79,91)(80,84)(81,88)(82,89)(86,90)(92,95)(93,94)Polycyclic presentation:
2^8,47|b^2=h,c^2=h,e^2=f,g^2=h,b^a=bf,c^a=cg,d^a=df,g^a=gh,i^a=i^46,c^b=cfh,d^b=dh,g^c=gh,i^c=i^46,e^d=eh1058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1044453);