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C3×#16811784 #23779446

order10230
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#16811784

Splittings

Fitting, socle, HallC3×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C3×C5
HallC3×#13133723 ⋊ C2
HallC3×D341 ⋊ C5
Hall#13133723 ⋊ C2×C3
HallD341 ⋊ C3×C5
HallC3×C31 ⋊ AGL(1,𝔽11)
HallC3×C11 ⋊ D31⋊C5
SylowC31 ⋊ C3×AGL(1,𝔽11)
SylowC11 ⋊ C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#16811784
commutator, cosocle, hypocenterC11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#16811772⋊C2, D3×#16811784, #16811784⋊D3, …
maximal normal subgroup ofC3×#16811772⋊C2, D3×#16811784, #16811784⋊D3, …
maximal quotient ofC3×#20291883, C2×C3×#16811784, C9×#16811784, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 45);