Finite Group Databasebeta

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C3×D7×D365 #44501407

order30660
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D7×D365

Splittings

Fitting, socle, HallC3×C5×C7×C73 ⋊ C22
derived, HallC5×C7×C73 ⋊ C22×C3
HallC3×C7×C73 ⋊ C2×D5
HallC3×C5×C73 ⋊ C2×D7
HallC7×C73 ⋊ C2×C3×D5
HallC5×C73 ⋊ C2×C3×D7
HallC3×C73 ⋊ D5×D7
HallC3×C5×C7 ⋊ C2×D73
SylowC73 ⋊ C3×D5×D7
HallC5×C7 ⋊ C2×C3×D73
HallC3×C7 ⋊ C2×D365
HallC3×C5 ⋊ D7×D73
SylowC7 ⋊ C2×C3×D365
SylowC5 ⋊ C3×D7×D73

Subgroups

subgroupG/H
center, hypercenterC3D7×D365
commutator, cosocle, hypocenterC5×C7×C73C22×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C73C22
LCSG ▷ C5×C7×C73
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

2760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 170);