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C3×C5⋊#10624391 #24926183

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

Aliases

direct productC3×C5⋊#10624391
unambiguous semidirect productC5⋊(C3×#10624391)

Splittings

Fitting, socleC3×C5×C112 ⋊ D3
derivedC5×C112⋊C3 ⋊ C2×C3
HallC3×C5×C112⋊C3 ⋊ C2
HallC3×C112⋊C3 ⋊ D5
HallC5×C112 ⋊ C3×D3
SylowC112 ⋊ C3×D15
SylowC5 ⋊ C3×#10624391

Subgroups

subgroupG/H
center, hypercenterC3C5⋊#10624391
commutator, cosocle, hypocenterC5×C112⋊C3C2×C3
FrattiniC1G
Fitting, socleC3×C5×C112D3
LCSG ▷ C5×C112⋊C3
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

372 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10624391⋊D5, C3×((C11⋊D11)⋊C3)⋊D5, C3×D5×#10624391, …
maximal normal subgroup ofC3×#10624391⋊D5, C3×((C11⋊D11)⋊C3)⋊D5, C3×D5×#10624391, …
maximal quotient ofC3×#20299971, C2×C3×C5⋊#10624391

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 132);