Finite Group Databasebeta

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C32×C7×D235 #44444109

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

Aliases

direct productC32×C7×D235
unambiguous semidirect productC5⋊(C32×C7×D47)
unambiguous semidirect productC47⋊(C32×C7×D5)

Splittings

Fitting, socle, HallC32×C5×C7×C47 ⋊ C2
derived, HallC5×C47 ⋊ C2×C32×C7
HallC32×C7×C47 ⋊ D5
HallC32×C5×C47 ⋊ C2×C7
HallC5×C7×C47 ⋊ C2×C32
HallC32×C47 ⋊ C7×D5
HallC7×C47 ⋊ C32×D5
HallC32×C5×C7 ⋊ D47
SylowC47 ⋊ C32×C7×D5
HallC32×C5 ⋊ C7×D47
HallC5×C7 ⋊ C32×D47
SylowC5 ⋊ C32×C7×D47

Subgroups

subgroupG/H
center, hypercenterC32×C7D235
commutator, cosocle, hypocenterC5×C47C2×C32×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C47C2
LCSG ▷ C5×C47
UCSC1 ◁ C32×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14805

Conjugacy classes & character table

7497 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 46);