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C3×#10624391⋊C5 #24926134

order10890
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#10624391⋊C5
unambiguous semidirect product#10624391⋊(C3×C5)
unambiguous semidirect product(C3×#10624391)⋊C5

Splittings

Fitting, socleC3×C112 ⋊ C5×D3
derivedC112⋊C3 ⋊ C2×C3×C5
HallC3×(C112⋊C3)⋊C5 ⋊ C2
HallC3×#10624391 ⋊ C5
HallC3×C112⋊C3 ⋊ C2×C5
Hall#10597243 ⋊ C3×D3
SylowC112 ⋊ C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC3#10624391⋊C5
commutator, cosocle, hypocenterC112⋊C3C2×C3×C5
FrattiniC1G
Fitting, socleC3×C112C5×D3
LCSG ▷ C112⋊C3
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(#10624391⋊C2)⋊C5, (#10624391⋊C5)⋊D3, D3×#10624391⋊C5, …
maximal normal subgroup ofC3×(#10624391⋊C2)⋊C5, (#10624391⋊C5)⋊D3, D3×#10624391⋊C5, …
maximal quotient ofC3×#13089712⋊C5, C2×C3×#10624391⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 83);