Finite Group Databasebeta

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C3×D5×D483 #44394580

order28980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D483
unambiguous semidirect product(C3×D5)⋊(C3×D161)
unambiguous semidirect product(D5×C23)⋊(C3×D21)

Splittings

Fitting, socle, HallC32×C5×C7×C23 ⋊ C22
derivedC3×C5×C7×C23 ⋊ C22×C3
HallC32×C7×C23 ⋊ C2×D5
HallC32×C5×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C2×D23
HallC32×C23 ⋊ D5×D7
HallC7×C23 ⋊ C3×D3×D5
HallC5×C23 ⋊ C2×C3×D21
HallC32×C7 ⋊ D5×D23
HallC32×C5 ⋊ C2×D161
HallC5×C7 ⋊ C2×C3×D69
SylowC23 ⋊ C3×D5×D21
SylowC32 ⋊ D5×D161
SylowC7 ⋊ C3×D5×D69
SylowC5 ⋊ C2×C3×D483

Subgroups

subgroupG/H
center, hypercenterC3D5×D483
commutator, cosocle, hypocenterC3×C5×C7×C23C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C3×C5×C7×C23
UCSC1 ◁ C3

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4830

Conjugacy classes & character table

2916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 249);