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C3×#10587380 #13108372

order1620
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#10587380

Splittings

Fitting, HallC3×C5×H(3,𝔽3) ⋊ C4
derivedC5×H(3,𝔽3) ⋊ C3×C4
SylowC3×H(3,𝔽3) ⋊ AGL(1,𝔽5)
SylowC5 ⋊ C3×#1084

Subgroups

subgroupG/H
center, hypercenterC32C3⋊ΓL(1,𝔽16)
commutator, hypocenterC5×H(3,𝔽3)C3×C4
FrattiniC3C3×C3⋊ΓL(1,𝔽16)
FittingC3×C5×H(3,𝔽3)C4
socleC32×C5C3⋊Dic3
prime radicalC3×D5×H(3,𝔽3)C2
cosocleD5×H(3,𝔽3)C2×C3
LCSG ▷ C5×H(3,𝔽3)
UCSC1 ◁ C32

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 135

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5), C3×AGL(1,𝔽5)×#272, C2×C3×#10587380, …
maximal normal subgroup ofC3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5), C3×AGL(1,𝔽5)×#272, C2×C3×#10587380, …
maximal quotient ofC2×C3×#10587380, #72247200, C3×#13108191, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 278);