Finite Group Databasebeta

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C3×C17×D365 #49151908

order37230
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×D365
unambiguous semidirect productC5⋊(C3×C17×D73)

Splittings

Fitting, socle, HallC3×C5×C17×C73 ⋊ C2
derived, HallC5×C73 ⋊ C2×C3×C17
HallC5×C17×C73 ⋊ C2×C3
HallC3×C17×C73 ⋊ D5
HallC17×C73 ⋊ C3×D5
HallC3×C5×C73 ⋊ C2×C17
HallC3×C5×C17 ⋊ D73
HallC3×C73 ⋊ D5×C17
HallC5×C17 ⋊ C3×D73
SylowC73 ⋊ C3×D5×C17
HallC3×C5 ⋊ C17×D73
SylowC5 ⋊ C3×C17×D73

Subgroups

subgroupG/H
center, hypercenterC3×C17D365
commutator, cosocle, hypocenterC5×C73C2×C3×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C73C2
LCSG ▷ C5×C73
UCSC1 ◁ C3×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18615

Conjugacy classes & character table

9384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37230, 7);