Finite Group Databasebeta

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C32×C5×D377 #46800258

order33930
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D377
unambiguous semidirect productC29⋊(C32×C5×D13)

Splittings

Fitting, socle, HallC32×C5×C13×C29 ⋊ C2
derived, HallC13×C29 ⋊ C2×C32×C5
HallC32×C13×C29 ⋊ C2×C5
HallC5×C13×C29 ⋊ C2×C32
HallC32×C5×C29 ⋊ D13
HallC32×C5×C13 ⋊ D29
HallC32×C29 ⋊ C5×D13
HallC5×C29 ⋊ C32×D13
HallC32×C13 ⋊ C5×D29
HallC5×C13 ⋊ C32×D29
SylowC29 ⋊ C32×C5×D13
SylowC13 ⋊ C32×C5×D29

Subgroups

subgroupG/H
center, hypercenterC32×C5D377
commutator, cosocle, hypocenterC13×C29C2×C32×C5
FrattiniC1G
Fitting, socleC32×C5×C13×C29C2
LCSG ▷ C13×C29
UCSC1 ◁ C32×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16965

Conjugacy classes & character table

8550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 44);