Finite Group Databasebeta

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C5×D373⋊C9 #46777060

order33570
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D373⋊C9
unambiguous semidirect productD373⋊(C5×C9)
unambiguous semidirect product(C373⋊C9)⋊(C2×C5)
unambiguous semidirect product(C5×D373)⋊C9

Splittings

derived, SylowC373 ⋊ C2×C5×C9
HallC5×C373⋊C9 ⋊ C2
HallC5×D373 ⋊ C9
HallC373⋊C9 ⋊ C2×C5
HallC5×C373 ⋊ C2×C9
HallD373 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5D373⋊C3
commutator, hypocenterC373C2×C5×C9
FrattiniC3C5×D373⋊C3
Fitting, socleC3×C5×C373C2×C3
prime radicalC3×C5×D373C3
cosocleC3×C373C2×C3×C5
LCSG ▷ C373
UCSC1 ◁ C3×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16785

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33570, 10);