Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C47×#2884 ⋊ C2 |
| Sylow | C47 ⋊ #60402 |
4778 conjugacy classes of subgroups; only the 727 normal subgroups are shown.
This group has 4778 conjugacy classes of subgroups — too many to draw. Only its 727 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 79 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)(48,53,54,49)(50,60,61,55)(51,63,64,56)(52,57,65,66)(58,70,72,67)(59,68,73,74)(62,69,75,76)(71,77,79,78);(48,52,54,65)(49,57,53,66)(50,59,61,73)(51,62,64,75)(55,68,60,74)(56,69,63,76)(58,71,72,79)(67,77,70,78);(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)(48,51)(49,56)(50,58)(52,62)(53,63)(54,64)(55,67)(57,69)(59,71)(60,70)(61,72)(65,75)(66,76)(68,77)(73,79)(74,78);(48,50)(49,55)(51,58)(52,59)(53,60)(54,61)(56,67)(57,68)(62,71)(63,70)(64,72)(65,73)(66,74)(69,77)(75,79)(76,78);(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)(48,49,54,53)(50,55,61,60)(51,56,64,63)(52,57,65,66)(58,70,72,67)(59,68,73,74)(62,69,75,76)(71,78,79,77)Polycyclic presentation:
2^8,47|a^2=h,d^2=h,e^2=h,b^a=bf,c^a=cg,i^a=i^46,g^b=gh,f^c=fh,i^c=i^46,e^d=eh1001 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036339);