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C3×C5×#10624391 #24926181

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

Aliases

direct productC3×C5×#10624391

Splittings

Fitting, socleC3×C5×C112 ⋊ D3
derivedC112⋊C3 ⋊ C2×C3×C5
HallC3×C5×C112⋊C3 ⋊ C2
HallC3×C112⋊C3 ⋊ C2×C5
HallC5×C112 ⋊ C3×D3
SylowC112 ⋊ C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC3×C5#10624391
commutator, cosocle, hypocenterC112⋊C3C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C112D3
LCSG ▷ C112⋊C3
UCSC1 ◁ C3×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×#10624391⋊C2, C3×#10624391⋊D5, C3×D5×#10624391, …
maximal normal subgroup ofC3×C5×#10624391⋊C2, C3×#10624391⋊D5, C3×D5×#10624391, …
maximal quotient ofC3×C5×#13089712, C2×C3×C5×#10624391

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 130);