Finite Group Databasebeta

← Prev (#44444104) Next (#44444106) →

C32×C5×C7×D47 #44444105

order29610
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C7×D47
unambiguous semidirect productC47⋊(C2×C32×C5×C7)

Splittings

Fitting, socle, HallC32×C5×C7×C47 ⋊ C2
derived, SylowC47 ⋊ C2×C32×C5×C7
HallC32×C7×C47 ⋊ C2×C5
HallC32×C5×C47 ⋊ C2×C7
HallC5×C7×C47 ⋊ C2×C32
HallC32×C47 ⋊ C2×C5×C7
HallC7×C47 ⋊ C2×C32×C5
HallC5×C47 ⋊ C2×C32×C7

Subgroups

subgroupG/H
center, hypercenterC32×C5×C7D47
commutator, cosocle, hypocenterC47C2×C32×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C47C2
LCSG ▷ C47
UCSC1 ◁ C32×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14805

Conjugacy classes & character table

7875 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 42);