Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C47×#3475 ⋊ C2 |
| Sylow | C47 ⋊ #62743 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D47 |
| commutator, socle, cosocle | C22×C47 | C26 |
| Frattini | C22 | C25×D47 |
| Fitting | C47×#3475 | C2 |
| hypercenter | #3475 | D47 |
| hypocenter | C47 | #62743 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ #3475 | |
At least 6428 conjugacy classes of subgroups; only the 3217 normal subgroups are shown.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 6 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)(64,67,68,75)(65,71,70,77)(66,74,73,79)(69,76,72,78);(49,55)(53,61)(54,58)(60,62);(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)(53,61)(56,63)(60,62)(65,70)(69,72)(71,77)(76,78);(48,51,52,59)(49,54,55,58)(50,56,57,63)(53,60,61,62)(66,73)(69,72)(74,79)(76,78);(48,50)(49,53)(51,56)(52,57)(54,60)(55,61)(58,62)(59,63)(64,66)(65,69)(67,74)(68,73)(70,72)(71,76)(75,79)(77,78);(48,49)(50,53)(51,58)(52,55)(54,59)(56,62)(57,61)(60,63)(64,65)(66,72)(67,71)(68,70)(69,73)(74,78)(75,77)(76,79)Polycyclic presentation:
2^8,47|c^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,c^b=cg,d^b=dh,i^d=i^461226 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1077123);