Finite Group Databasebeta

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C5×C9×D377 #46800219

order33930
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D377
unambiguous semidirect productC29⋊(C5×C9×D13)

Splittings

Fitting, HallC5×C9×C13×C29 ⋊ C2
derived, HallC13×C29 ⋊ C2×C5×C9
HallC9×C13×C29 ⋊ C2×C5
HallC5×C13×C29 ⋊ C2×C9
HallC5×C9×C29 ⋊ D13
HallC5×C9×C13 ⋊ D29
HallC9×C29 ⋊ C5×D13
HallC5×C29 ⋊ C9×D13
HallC9×C13 ⋊ C5×D29
HallC5×C13 ⋊ C9×D29
SylowC29 ⋊ C5×C9×D13
SylowC13 ⋊ C5×C9×D29

Subgroups

subgroupG/H
center, hypercenterC5×C9D377
commutator, hypocenterC13×C29C2×C5×C9
FrattiniC3C3×C5×D377
FittingC5×C9×C13×C29C2
socleC3×C5×C13×C29C2×C3
prime radicalC3×C5×D377C3
cosocleC3×C13×C29C2×C3×C5
LCSG ▷ C13×C29
UCSC1 ◁ C5×C9

48 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, 5);