Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C47 ⋊ #60113 |
2564 conjugacy classes of subgroups.
| 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)(50,61)(55,69)(59,73)(60,74)(62,63)(68,78)(72,79)(75,76);(51,64)(56,70)(60,74)(65,66)(68,78)(71,77)(72,79)(75,76);(48,51)(49,56)(50,60)(52,65)(53,66)(54,64)(55,68)(57,71)(58,70)(59,72)(61,74)(62,75)(63,76)(67,77)(69,78)(73,79);(48,50,52,62,54,61,53,63)(49,55,57,59,58,69,67,73)(51,60,65,75,64,74,66,76)(56,68,71,72,70,78,77,79);(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)(48,49,53,57,54,58,52,67)(50,59,63,69,61,73,62,55)(51,56,66,71,64,70,65,77)(60,72,76,78,74,79,75,68)Polycyclic presentation:
2^8,47|a^2=g,b^2=f,f^2=h,g^2=h,b^a=bf,f^a=fh,i^a=i^46,e^b=eh,d^c=dh1646 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033270);