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C3×#16811780 #23779442

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

Aliases

direct productC3×#16811780

Splittings

Fitting, socle, HallC3×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C3×C5
HallC3×#13133724 ⋊ C2
HallC3×D11×C31 ⋊ C5
Hall#13133724 ⋊ C2×C3
HallD11×C31 ⋊ C3×C5
HallC3×C31 ⋊ AGL(1,𝔽11)
HallC3×D11 ⋊ ΓL(1,𝔽32)
HallC3×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C3×AGL(1,𝔽11)
HallD11 ⋊ C3×ΓL(1,𝔽32)
SylowC11 ⋊ C2×C3×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC3#16811780
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

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#16811774⋊C2, #16811780⋊D3, D3×#16811780, …
maximal normal subgroup ofC3×#16811774⋊C2, #16811780⋊D3, D3×#16811780, …
maximal quotient ofC3×#20291879, C2×C3×#16811780, C9×#16811780, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 41);