Finite Group Databasebeta

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C5×C3⋊#10587723 #22551256

order8190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊#10587723
unambiguous semidirect productC3⋊(C5×#10587723)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C2×C3
derivedC3×C7×C13 ⋊ C2×C3×C5
HallC3×C5×#63271 ⋊ C2
HallC3×#63271 ⋊ C2×C5
HallC5×C7×C13 ⋊ C3×D3
HallC7×C13 ⋊ C3×C5×D3
HallC5×C13 ⋊ C3⋊AGL(1,𝔽7)
HallC5×C7 ⋊ C3⋊(D13⋊C3)
SylowC13 ⋊ C5×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C5×C3⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊#10587723
commutator, hypocenterC3×C7×C13C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

270 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#10587717⋊D3, C5×#10587721⋊D3, C5×D3×#10587723, …
maximal normal subgroup ofC5×#10587717⋊D3, C5×#10587721⋊D3, C5×D3×#10587723, …
maximal quotient ofC5×C3⋊#11763964, C2×C5×C3⋊#10587723

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 90);